matroids-from-graphs-12vertices.md

Matroids from graphs on 12 vertices

• We consider all the 3-connected trivalent simple graphs on 12 vertices. We used the list of such graph from here.

• We call the graphs Graph12i, where 12 refers to the number of vertices and i is just the index for our list. We describe each graph via its list of edges.

• For each graph in the list, we used the algorithm from matroid-from-graph.m2 to construct a graph curve whose associated graph is our graph Graph12i.

• Our algorithm then intersects the generated graph curve with a randomly generated (i.e. generic) hyperplane. For each graph, we record the equation of the hyperplane that was generated.

• We also record the coordinates of the points that we got in this intersection (i.e. in the hyperplane section that we get by intersecting our graph curve with a hyperplane). Because we started with a graph with 2g-2 = 12 vertices, the graph curve that we get always has genus g = 7 and degree 2g-2 = 12, and lies in projective space P^{g-1} = P^6, so our hyperplane section consists of 12 points in P^6.

• Our algorithm from matroid-from-graph.m2 then extracts a self-dual matroid on 12 elements {0,1,...,11} from the configuration of the points that we generated. The matroid has rank 6 because the points lie and span our hyperplane = P^5 inside P^6.

• We describe the matroid that we get by saying how many bases and non-bases it has. We also enumerate the circuits of each matroid, ordered by size.

• We also note here that some of the graphs give isomorphic matroids. We record this here, as follows: if indices i and j appear in the same set below, it means that the graphs Graph12i and Graph12j give isomorphic matroids:

  • {1, 3, 8, 17}

  • {2, 7}

  • {4, 6, 29}

  • {5, 31}

  • {9, 22}

  • {12, 14}

  • {23, 30}

  • {36, 39}

  • {50, 52}

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1. Graph121:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,1}, {4,5}, {5,6}, {6,3}, {6,7}, {7,8}, {8,5}, {8,9}, {9,10}, {10,7}, {10,11}, {11,9}, {0,11}

• Randomly generated (generic) hyperplane:

  71*a + 79*b + 3*c + 53*d + 18*e + 83*f + 97*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 1 : 1 : -71/83 : 0]

  [1 : 0 : 0 : -154/71 : -154/71 : 1 : 0]

  [1 : 0 : 0 : 0 : 0 : -71/83 : 0]

  [1 : -71/91 : 0 : 71/91 : 71/91 : -71/91 : 0]

  [1 : -83/79 : 0 : -1 : -1 : 1 : 0]

  [0 : 1 : 79/159 : 0 : 79/159 : -79/159 : -79/159]

  [0 : 1 : 13/21 : -34/21 : -1 : 1 : -13/21]

  [0 : 0 : 1 : -1 : -49/54 : 49/54 : -5/54]

  [0 : 0 : 1 : 0 : 1/54 : -1/54 : -1/54]

  [0 : 0 : 1 : 3/109 : 3/109 : -3/109 : -3/109]

  [0 : 0 : 1 : -1 : -1 : 1 : -15/97]

  [0 : 0 : 0 : 1 : 1 : -1 : 12/97]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 486 bases, 438 non-bases

  • circuits:

    • 2 circuits of size 3:

      {0, 1, 2}, {9, 10, 11}

    • 8 circuits of size 4:

      {0, 1, 3, 4}, {0, 2, 3, 4}, {1, 2, 3, 4}, {3, 4, 5, 6}, {5, 6, 7, 8}, {7, 8, 9, 10}, {7, 8, 9, 11}, {7, 8, 10, 11}

    • 14 circuits of size 5:

      {0, 1, 3, 5, 6}, {0, 2, 3, 5, 6}, {1, 2, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 4, 5, 6}, {1, 2, 4, 5, 6}, {3, 4, 5, 7, 8}, {3, 4, 6, 7, 8}, {5, 6, 7, 9, 10}, {5, 6, 8, 9, 10}, {5, 6, 7, 9, 11}, {5, 6, 8, 9, 11}, {5, 6, 7, 10, 11}, {5, 6, 8, 10, 11}

    • 24 circuits of size 6:

      {0, 1, 3, 5, 7, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 5, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {3, 4, 5, 7, 9, 10}, {3, 4, 6, 7, 9, 10}, {3, 4, 5, 8, 9, 10}, {3, 4, 6, 8, 9, 10}, {3, 4, 5, 7, 9, 11}, {3, 4, 6, 7, 9, 11}, {3, 4, 5, 8, 9, 11}, {3, 4, 6, 8, 9, 11}, {3, 4, 5, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {3, 4, 5, 8, 10, 11}, {3, 4, 6, 8, 10, 11}

    • 72 circuits of size 7:

      {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}

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2. Graph122:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,1}, {4,5}, {5,6}, {6,3}, {6,7}, {5,8}, {7,9}, {7,10}, {8,9}, {8,10}, {9,11}, {10,11}, {0,11}

• Randomly generated (generic) hyperplane:

  91*a + 95*b + 35*c + 64*d + 83*e + 32*f + 9*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 1 : 67/19 : -67/19 : 1 : 0]

  [0 : 0 : 1 : -67/32 : 0 : 99/32 : 0]

  [0 : 0 : 1 : 118/19 : -99/19 : 0 : 0]

  [1 : 0 : -123/118 : 1 : -123/118 : -1 : 0]

  [1 : 0 : 0 : -91/32 : 0 : 91/32 : 0]

  [1 : -91/9 : 91/9 : -91/9 : 91/9 : 91/9 : 0]

  [1 : -1/19 : -1 : 1 : -1 : -1 : 0]

  [0 : 1 : 19/5 : 19/5 : -19/5 : -19/5 : -19/5]

  [0 : 1 : -1 : 20/17 : -20/17 : -20/17 : 0]

  [0 : 0 : 1 : 26/51 : -26/51 : -26/51 : -1]

  [0 : 1 : -1 : 1 : -1 : -1 : -1]

  [0 : 0 : 1 : 13/30 : -13/30 : -13/30 : -43/30]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 540 bases, 384 non-bases

  • circuits:

    • 1 circuit of size 3:

      {0, 1, 2}

    • 9 circuits of size 4:

      {0, 1, 3, 4}, {0, 2, 3, 4}, {1, 2, 3, 4}, {3, 4, 5, 6}, {7, 8, 9, 10}, {7, 8, 9, 11}, {7, 8, 10, 11}, {7, 9, 10, 11}, {8, 9, 10, 11}

    • 16 circuits of size 5:

      {0, 1, 3, 5, 6}, {0, 2, 3, 5, 6}, {1, 2, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 4, 5, 6}, {1, 2, 4, 5, 6}, {5, 6, 7, 8, 9}, {5, 6, 7, 8, 10}, {5, 6, 7, 9, 10}, {5, 6, 8, 9, 10}, {5, 6, 7, 8, 11}, {5, 6, 7, 9, 11}, {5, 6, 8, 9, 11}, {5, 6, 7, 10, 11}, {5, 6, 8, 10, 11}, {5, 6, 9, 10, 11}

    • 20 circuits of size 6:

      {3, 4, 5, 7, 8, 9}, {3, 4, 6, 7, 8, 9}, {3, 4, 5, 7, 8, 10}, {3, 4, 6, 7, 8, 10}, {3, 4, 5, 7, 9, 10}, {3, 4, 6, 7, 9, 10}, {3, 4, 5, 8, 9, 10}, {3, 4, 6, 8, 9, 10}, {3, 4, 5, 7, 8, 11}, {3, 4, 6, 7, 8, 11}, {3, 4, 5, 7, 9, 11}, {3, 4, 6, 7, 9, 11}, {3, 4, 5, 8, 9, 11}, {3, 4, 6, 8, 9, 11}, {3, 4, 5, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {3, 4, 5, 8, 10, 11}, {3, 4, 6, 8, 10, 11}, {3, 4, 5, 9, 10, 11}, {3, 4, 6, 9, 10, 11}

    • 120 circuits of size 7:

      {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {1, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {1, 2, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}

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3. Graph123:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,1}, {4,5}, {5,6}, {6,3}, {6,7}, {5,8}, {7,9}, {8,9}, {8,10}, {9,10}, {10,11}, {11,7}, {0,11}

• Randomly generated (generic) hyperplane:

  50*a + 9*b + 60*c + 77*d + 39*e + 29*f + 83*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 1 : 1 : -4 : 0]

  [1 : 0 : 0 : -79/116 : -79/116 : 1 : 0]

  [1 : 0 : 0 : 0 : 0 : -50/29 : 0]

  [1 : 25/39 : 0 : -25/39 : -25/39 : 25/39 : 0]

  [1 : 37/9 : 0 : -1 : -1 : 1 : 0]

  [0 : 1 : -1/17 : 0 : -1/17 : 1/17 : -1/17]

  [0 : 1 : 13/11 : -24/11 : -1 : 1 : 13/11]

  [0 : 0 : 1 : -35/2 : -33/2 : 33/2 : 35/2]

  [0 : 0 : 1 : 0 : -20/31 : 20/31 : -20/31]

  [0 : 0 : 1 : 0 : -6 : 6 : 0]

  [0 : 0 : 0 : 0 : 1 : -1 : -10/83]

  [0 : 0 : 0 : 1 : 1 : -1 : -87/83]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 486 bases, 438 non-bases

  • circuits:

    • 2 circuits of size 3:

      {0, 1, 2}, {8, 9, 10}

    • 8 circuits of size 4:

      {0, 1, 3, 4}, {0, 2, 3, 4}, {1, 2, 3, 4}, {3, 4, 5, 6}, {5, 6, 7, 11}, {7, 8, 9, 11}, {7, 8, 10, 11}, {7, 9, 10, 11}

    • 14 circuits of size 5:

      {0, 1, 3, 5, 6}, {0, 2, 3, 5, 6}, {1, 2, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 4, 5, 6}, {1, 2, 4, 5, 6}, {5, 6, 7, 8, 9}, {5, 6, 7, 8, 10}, {5, 6, 7, 9, 10}, {3, 4, 5, 7, 11}, {3, 4, 6, 7, 11}, {5, 6, 8, 9, 11}, {5, 6, 8, 10, 11}, {5, 6, 9, 10, 11}

    • 24 circuits of size 6:

      {3, 4, 5, 7, 8, 9}, {3, 4, 6, 7, 8, 9}, {3, 4, 5, 7, 8, 10}, {3, 4, 6, 7, 8, 10}, {3, 4, 5, 7, 9, 10}, {3, 4, 6, 7, 9, 10}, {0, 1, 3, 5, 7, 11}, {0, 2, 3, 5, 7, 11}, {1, 2, 3, 5, 7, 11}, {0, 1, 4, 5, 7, 11}, {0, 2, 4, 5, 7, 11}, {1, 2, 4, 5, 7, 11}, {0, 1, 3, 6, 7, 11}, {0, 2, 3, 6, 7, 11}, {1, 2, 3, 6, 7, 11}, {0, 1, 4, 6, 7, 11}, {0, 2, 4, 6, 7, 11}, {1, 2, 4, 6, 7, 11}, {3, 4, 5, 8, 9, 11}, {3, 4, 6, 8, 9, 11}, {3, 4, 5, 8, 10, 11}, {3, 4, 6, 8, 10, 11}, {3, 4, 5, 9, 10, 11}, {3, 4, 6, 9, 10, 11}

    • 72 circuits of size 7:

      {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {1, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {1, 2, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}

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4. Graph124:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,1}, {4,5}, {3,6}, {5,7}, {5,8}, {6,7}, {6,8}, {8,9}, {7,10}, {9,10}, {10,11}, {11,9}, {0,11}

• Randomly generated (generic) hyperplane:

  20*a + 72*b + 67*c + 11*d + 68*e + 81*f + 5*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 3/26 : 3/26 : 0 : -1 : 0]

  [0 : 0 : 1 : 7/46 : 0 : -39/46 : 0]

  [0 : 1 : 0 : 9/92 : 0 : -83/92 : 0]

  [0 : 1 : 83/25 : -58/25 : 0 : -83/25 : 0]

  [0 : 0 : 1 : 14/11 : 0 : -1 : 0]

  [1 : 0 : 0 : -8 : 1 : 0 : 0]

  [1 : 27/29 : 27/29 : -1 : -1 : -27/29 : 1]

  [1 : 0 : 0 : -1 : -23/131 : 0 : 77/131]

  [1 : -11/25 : -11/25 : -11/25 : 3/25 : 11/25 : 11/25]

  [0 : 1 : 1 : 1 : -16/17 : -1 : -1]

  [0 : 0 : 0 : 0 : 1 : 0 : -68/5]

  [0 : 1 : 1 : 1 : -23/21 : -1 : 23/21]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 540 bases, 384 non-bases

  • circuits:

    • 2 circuits of size 3:

      {0, 1, 2}, {9, 10, 11}

    • 4 circuits of size 4:

      {0, 1, 3, 4}, {0, 2, 3, 4}, {1, 2, 3, 4}, {5, 6, 7, 8}

    • 16 circuits of size 5:

      {3, 4, 5, 6, 7}, {3, 4, 5, 6, 8}, {3, 4, 5, 7, 8}, {3, 4, 6, 7, 8}, {5, 6, 7, 9, 10}, {5, 6, 8, 9, 10}, {5, 7, 8, 9, 10}, {6, 7, 8, 9, 10}, {5, 6, 7, 9, 11}, {5, 6, 8, 9, 11}, {5, 7, 8, 9, 11}, {6, 7, 8, 9, 11}, {5, 6, 7, 10, 11}, {5, 6, 8, 10, 11}, {5, 7, 8, 10, 11}, {6, 7, 8, 10, 11}

    • 42 circuits of size 6:

      {0, 1, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 6, 8}, {0, 1, 4, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 5, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {3, 4, 5, 6, 9, 10}, {3, 4, 5, 7, 9, 10}, {3, 4, 6, 7, 9, 10}, {3, 4, 5, 8, 9, 10}, {3, 4, 6, 8, 9, 10}, {3, 4, 7, 8, 9, 10}, {3, 4, 5, 6, 9, 11}, {3, 4, 5, 7, 9, 11}, {3, 4, 6, 7, 9, 11}, {3, 4, 5, 8, 9, 11}, {3, 4, 6, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {3, 4, 5, 6, 10, 11}, {3, 4, 5, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {3, 4, 5, 8, 10, 11}, {3, 4, 6, 8, 10, 11}, {3, 4, 7, 8, 10, 11}

    • 108 circuits of size 7:

      {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {1, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 3, 7, 8, 9, 11}, {1, 2, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 4, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {1, 2, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}

---

---

5. Graph125:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {1,4}, {4,5}, {4,6}, {3,5}, {3,6}, {5,8}, {6,7}, {8,9}, {8,10}, {7,9}, {7,10}, {9,11}, {10,11}, {0,11}

• Randomly generated (generic) hyperplane:

  69*a + 5*b + 68*c + 53*d + 56*e + 89*f + 98*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : 0 : 0 : -167/187 : 20/187]

  [1 : 0 : 167/30 : 0 : 0 : 0 : -137/30]

  [1 : 0 : 20/157 : 0 : 0 : -137/157 : 0]

  [0 : 1 : -94/157 : 0 : 0 : 63/157 : 0]

  [0 : 1 : 1/6 : 0 : 0 : 0 : -1/6]

  [0 : 1 : -5/68 : 0 : 0 : 0 : 0]

  [0 : 1 : 94/119 : 0 : 0 : 25/119 : -94/119]

  [0 : 0 : 1 : 119/53 : 0 : -1 : -1]

  [0 : 0 : 1 : 34/39 : 34/39 : -34/39 : -34/39]

  [0 : 0 : 1 : 1 : 33/28 : -1 : -1]

  [0 : 0 : 0 : 1 : 53/131 : -53/131 : -53/131]

  [0 : 0 : 0 : 0 : 1 : -56/187 : -56/187]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 600 bases, 324 non-bases

  • circuits:

    • 1 circuit of size 3:

      {0, 1, 2}

    • 6 circuits of size 4:

      {3, 4, 5, 6}, {7, 8, 9, 10}, {7, 8, 9, 11}, {7, 8, 10, 11}, {7, 9, 10, 11}, {8, 9, 10, 11}

    • 12 circuits of size 5:

      {0, 1, 3, 4, 5}, {0, 2, 3, 4, 5}, {1, 2, 3, 4, 5}, {0, 1, 3, 4, 6}, {0, 2, 3, 4, 6}, {1, 2, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 5, 6}, {1, 2, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 4, 5, 6}, {1, 2, 4, 5, 6}

    • 40 circuits of size 6:

      {3, 4, 5, 7, 8, 9}, {3, 4, 6, 7, 8, 9}, {3, 5, 6, 7, 8, 9}, {4, 5, 6, 7, 8, 9}, {3, 4, 5, 7, 8, 10}, {3, 4, 6, 7, 8, 10}, {3, 5, 6, 7, 8, 10}, {4, 5, 6, 7, 8, 10}, {3, 4, 5, 7, 9, 10}, {3, 4, 6, 7, 9, 10}, {3, 5, 6, 7, 9, 10}, {4, 5, 6, 7, 9, 10}, {3, 4, 5, 8, 9, 10}, {3, 4, 6, 8, 9, 10}, {3, 5, 6, 8, 9, 10}, {4, 5, 6, 8, 9, 10}, {3, 4, 5, 7, 8, 11}, {3, 4, 6, 7, 8, 11}, {3, 5, 6, 7, 8, 11}, {4, 5, 6, 7, 8, 11}, {3, 4, 5, 7, 9, 11}, {3, 4, 6, 7, 9, 11}, {3, 5, 6, 7, 9, 11}, {4, 5, 6, 7, 9, 11}, {3, 4, 5, 8, 9, 11}, {3, 4, 6, 8, 9, 11}, {3, 5, 6, 8, 9, 11}, {4, 5, 6, 8, 9, 11}, {3, 4, 5, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {3, 5, 6, 7, 10, 11}, {4, 5, 6, 7, 10, 11}, {3, 4, 5, 8, 10, 11}, {3, 4, 6, 8, 10, 11}, {3, 5, 6, 8, 10, 11}, {4, 5, 6, 8, 10, 11}, {3, 4, 5, 9, 10, 11}, {3, 4, 6, 9, 10, 11}, {3, 5, 6, 9, 10, 11}, {4, 5, 6, 9, 10, 11}

    • 180 circuits of size 7:

      {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {1, 2, 3, 4, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {1, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 1, 5, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {1, 2, 5, 6, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {1, 2, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 1, 5, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 2, 3, 4, 8, 9, 10}, {1, 2, 3, 4, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 1, 5, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 2, 3, 4, 8, 9, 11}, {1, 2, 3, 4, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 5, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 2, 3, 4, 9, 10, 11}, {1, 2, 3, 4, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}

---

---

6. Graph126:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {1,6}, {6,0}, {6,7}, {2,7}, {7,8}, {8,9}, {9,10}, {10,8}, {4,10}, {3,11}, {5,11}, {9,11}

• Randomly generated (generic) hyperplane:

  57*a + 43*b + 70*c + 33*d + 8*e + 23*f + 4*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 0 : 0 : -43/12 : 0 : -43/12]

  [0 : 1 : -43/74 : 0 : -43/74 : 0 : 43/74]

  [0 : 1 : -1 : 31/29 : -1 : 0 : -2/29]

  [1 : 0 : 0 : -57/29 : 0 : 0 : 57/29]

  [1 : 0 : 0 : -57/68 : -57/68 : -57/68 : -57/68]

  [1 : 0 : 0 : 1 : -113/12 : 1 : -113/12]

  [0 : 1 : -31/74 : 0 : -105/74 : 0 : -43/74]

  [0 : 1 : -1 : 43/41 : -39/41 : 0 : 0]

  [0 : 0 : 0 : 1 : -6/35 : -41/35 : -41/35]

  [0 : 0 : 0 : 1 : 0 : -11/9 : -11/9]

  [0 : 0 : 0 : 1 : -33/35 : -33/35 : -33/35]

  [1 : 0 : 0 : 1 : 0 : -86/27 : -113/27]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 540 bases, 384 non-bases

  • circuits:

    • 2 circuits of size 3:

      {0, 1, 6}, {8, 9, 10}

    • 4 circuits of size 4:

      {0, 1, 2, 7}, {0, 2, 6, 7}, {1, 2, 6, 7}, {3, 4, 5, 11}

    • 16 circuits of size 5:

      {2, 3, 4, 5, 7}, {3, 4, 5, 8, 9}, {3, 4, 5, 8, 10}, {3, 4, 5, 9, 10}, {2, 3, 4, 7, 11}, {2, 3, 5, 7, 11}, {2, 4, 5, 7, 11}, {3, 4, 8, 9, 11}, {3, 5, 8, 9, 11}, {4, 5, 8, 9, 11}, {3, 4, 8, 10, 11}, {3, 5, 8, 10, 11}, {4, 5, 8, 10, 11}, {3, 4, 9, 10, 11}, {3, 5, 9, 10, 11}, {4, 5, 9, 10, 11}

    • 42 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 7}, {0, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 7}, {2, 3, 4, 7, 8, 9}, {2, 3, 5, 7, 8, 9}, {2, 4, 5, 7, 8, 9}, {2, 3, 4, 7, 8, 10}, {2, 3, 5, 7, 8, 10}, {2, 4, 5, 7, 8, 10}, {2, 3, 4, 7, 9, 10}, {2, 3, 5, 7, 9, 10}, {2, 4, 5, 7, 9, 10}, {0, 1, 2, 3, 4, 11}, {0, 1, 2, 3, 5, 11}, {0, 1, 2, 4, 5, 11}, {0, 2, 3, 4, 6, 11}, {1, 2, 3, 4, 6, 11}, {0, 2, 3, 5, 6, 11}, {1, 2, 3, 5, 6, 11}, {0, 2, 4, 5, 6, 11}, {1, 2, 4, 5, 6, 11}, {0, 1, 3, 4, 7, 11}, {0, 1, 3, 5, 7, 11}, {0, 1, 4, 5, 7, 11}, {0, 3, 4, 6, 7, 11}, {1, 3, 4, 6, 7, 11}, {0, 3, 5, 6, 7, 11}, {1, 3, 5, 6, 7, 11}, {0, 4, 5, 6, 7, 11}, {1, 4, 5, 6, 7, 11}, {2, 3, 7, 8, 9, 11}, {2, 4, 7, 8, 9, 11}, {2, 5, 7, 8, 9, 11}, {2, 3, 7, 8, 10, 11}, {2, 4, 7, 8, 10, 11}, {2, 5, 7, 8, 10, 11}, {2, 3, 7, 9, 10, 11}, {2, 4, 7, 9, 10, 11}, {2, 5, 7, 9, 10, 11}

    • 108 circuits of size 7:

      {0, 1, 2, 3, 4, 8, 9}, {0, 1, 2, 3, 5, 8, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 4, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {0, 4, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 8, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {0, 4, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 4, 9, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {0, 4, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 3, 8, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {0, 5, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 8, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {0, 4, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {0, 5, 6, 7, 8, 10, 11}, {1, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 3, 9, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {0, 4, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {0, 5, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}

---

---

7. Graph127:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,0}, {0,7}, {2,7}, {7,8}, {1,8}, {8,10}, {3,10}, {9,10}, {6,9}, {9,11}, {4,11}, {11,5}

• Randomly generated (generic) hyperplane:

  57*a + 52*b + 75*c + 6*d + 31*e + 66*f + 25*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 1 : -75/37 : -75/37 : 0 : 0]

  [1 : 0 : -1/75 : 0 : -1 : 0 : -1]

  [1 : 0 : -5/14 : -19/14 : -1 : 0 : 5/14]

  [0 : 1 : -27/14 : -27/14 : 1 : 0 : 41/14]

  [0 : 1 : -59/23 : -59/23 : -59/23 : 82/23 : 0]

  [0 : 1 : 0 : 0 : 0 : -77/41 : 118/41]

  [0 : 1 : -11/16 : -11/16 : -11/16 : 0 : 1]

  [1 : 0 : 0 : -57/37 : -57/37 : 0 : 0]

  [1 : 0 : 0 : 0 : -57/56 : 0 : -57/56]

  [0 : 1 : -52/87 : -52/87 : -52/87 : 0 : 52/87]

  [0 : 1 : 0 : 0 : -13/14 : 0 : -13/14]

  [0 : 0 : 1 : 1 : 1 : -87/41 : 46/41]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 540 bases, 384 non-bases

  • circuits:

    • 1 circuit of size 3:

      {4, 5, 11}

    • 9 circuits of size 4:

      {0, 1, 2, 7}, {0, 1, 2, 8}, {0, 1, 7, 8}, {0, 2, 7, 8}, {1, 2, 7, 8}, {4, 5, 6, 9}, {3, 6, 9, 10}, {4, 6, 9, 11}, {5, 6, 9, 11}

    • 16 circuits of size 5:

      {0, 1, 2, 3, 10}, {3, 4, 5, 6, 10}, {0, 1, 3, 7, 10}, {0, 2, 3, 7, 10}, {1, 2, 3, 7, 10}, {0, 1, 3, 8, 10}, {0, 2, 3, 8, 10}, {1, 2, 3, 8, 10}, {0, 3, 7, 8, 10}, {1, 3, 7, 8, 10}, {2, 3, 7, 8, 10}, {3, 4, 5, 9, 10}, {3, 4, 6, 10, 11}, {3, 5, 6, 10, 11}, {3, 4, 9, 10, 11}, {3, 5, 9, 10, 11}

    • 20 circuits of size 6:

      {0, 1, 2, 3, 6, 9}, {0, 1, 3, 6, 7, 9}, {0, 2, 3, 6, 7, 9}, {1, 2, 3, 6, 7, 9}, {0, 1, 3, 6, 8, 9}, {0, 2, 3, 6, 8, 9}, {1, 2, 3, 6, 8, 9}, {0, 3, 6, 7, 8, 9}, {1, 3, 6, 7, 8, 9}, {2, 3, 6, 7, 8, 9}, {0, 1, 2, 6, 9, 10}, {0, 1, 6, 7, 9, 10}, {0, 2, 6, 7, 9, 10}, {1, 2, 6, 7, 9, 10}, {0, 1, 6, 8, 9, 10}, {0, 2, 6, 8, 9, 10}, {1, 2, 6, 8, 9, 10}, {0, 6, 7, 8, 9, 10}, {1, 6, 7, 8, 9, 10}, {2, 6, 7, 8, 9, 10}

    • 120 circuits of size 7:

      {0, 1, 2, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 3, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 5, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {1, 2, 3, 4, 5, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 1, 2, 4, 5, 6, 10}, {0, 1, 4, 5, 6, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 4, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 1, 3, 4, 6, 7, 11}, {0, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 1, 3, 5, 6, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 4, 9, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 2, 3, 4, 8, 9, 11}, {1, 2, 3, 4, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {2, 3, 4, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 5, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 4, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {0, 5, 6, 7, 8, 10, 11}, {1, 5, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {1, 2, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {2, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}

---

---

8. Graph128:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {4,5}, {5,6}, {6,3}, {6,7}, {7,5}, {2,8}, {8,9}, {9,1}, {9,10}, {10,8}, {0,11}, {7,11}, {10,11}

• Randomly generated (generic) hyperplane:

  61*a + 58*b + 89*c + 77*d + 26*e + 41*f + 37*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 1 : -1 : 0 : 0 : -12/37]

  [0 : 0 : 1 : -89/77 : 0 : 0 : 0]

  [0 : 0 : 1 : -89/73 : 0 : 89/73 : -89/73]

  [1 : 0 : -51/8 : 51/8 : 0 : -43/8 : 51/8]

  [1 : 0 : 102/25 : -102/25 : 0 : 1 : -102/25]

  [1 : -127/99 : -1 : 1 : 0 : -28/99 : 1]

  [1 : -86/99 : -1 : 1 : 0 : -86/99 : 1]

  [1 : -1 : -1 : 1 : 0 : -28/41 : 1]

  [0 : 0 : 0 : 1 : -73/22 : 51/22 : -51/22]

  [0 : 0 : 0 : 1 : -7/2 : 7/2 : -7/2]

  [0 : 0 : 0 : 1 : -1 : -51/4 : 51/4]

  [0 : 0 : 0 : 0 : 0 : 1 : -41/37]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 486 bases, 438 non-bases

  • circuits:

    • 2 circuits of size 3:

      {5, 6, 7}, {8, 9, 10}

    • 8 circuits of size 4:

      {3, 4, 5, 6}, {3, 4, 5, 7}, {3, 4, 6, 7}, {1, 2, 8, 9}, {1, 2, 8, 10}, {1, 2, 9, 10}, {0, 1, 2, 11}, {0, 3, 4, 11}

    • 14 circuits of size 5:

      {0, 1, 2, 3, 4}, {1, 2, 3, 4, 11}, {0, 3, 5, 6, 11}, {0, 4, 5, 6, 11}, {0, 3, 5, 7, 11}, {0, 4, 5, 7, 11}, {0, 3, 6, 7, 11}, {0, 4, 6, 7, 11}, {0, 1, 8, 9, 11}, {0, 2, 8, 9, 11}, {0, 1, 8, 10, 11}, {0, 2, 8, 10, 11}, {0, 1, 9, 10, 11}, {0, 2, 9, 10, 11}

    • 24 circuits of size 7:

      {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 8, 9}, {0, 2, 3, 4, 8, 9}, {0, 1, 3, 4, 8, 10}, {0, 2, 3, 4, 8, 10}, {0, 1, 3, 4, 9, 10}, {0, 2, 3, 4, 9, 10}, {1, 2, 3, 5, 6, 11}, {1, 2, 4, 5, 6, 11}, {1, 2, 3, 5, 7, 11}, {1, 2, 4, 5, 7, 11}, {1, 2, 3, 6, 7, 11}, {1, 2, 4, 6, 7, 11}, {1, 3, 4, 8, 9, 11}, {2, 3, 4, 8, 9, 11}, {1, 3, 4, 8, 10, 11}, {2, 3, 4, 8, 10, 11}, {1, 3, 4, 9, 10, 11}, {2, 3, 4, 9, 10, 11}

    • 72 circuits of size 7:

      {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {1, 4, 5, 6, 9, 10, 11}, {2, 4, 5, 6, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {2, 4, 5, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 3, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}

---

---

9. Graph129:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,1}, {4,5}, {5,6}, {6,7}, {7,3}, {7,8}, {8,9}, {9,5}, {8,11}, {11,10}, {10,9}, {6,11}, {0,10}

• Randomly generated (generic) hyperplane:

  36*a + 95*b + 85*c + 12*d + 99*e + 6*f + 60*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : 12/29 : -12/29 : 0 : 0]

  [1 : -18/91 : 0 : 18/91 : -18/91 : 0 : 0]

  [1 : -123/95 : 0 : -1 : 1 : 0 : 0]

  [0 : 1 : 0 : 0 : -95/33 : 95/33 : 95/33]

  [0 : 1 : 0 : 64/27 : 1 : -91/27 : -91/27]

  [0 : 0 : 0 : 1 : 0 : -1 : -1/10]

  [0 : 0 : 1 : 41/6 : 0 : -47/6 : -2]

  [0 : 0 : 1 : 1 : 35/33 : -101/33 : -101/33]

  [0 : 0 : 1 : 25/93 : -25/93 : -25/93 : -1]

  [0 : 0 : 0 : 1 : -1 : -1 : 31/20]

  [0 : 0 : 0 : 1 : -1 : 29/22 : 29/22]

  [0 : 0 : 1 : 0 : 0 : -25/66 : -91/66]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 594 bases, 330 non-bases

  • circuits:

    • 1 circuit of size 3:

      {0, 1, 2}

    • 5 circuits of size 4:

      {0, 1, 3, 4}, {0, 2, 3, 4}, {1, 2, 3, 4}, {6, 7, 8, 11}, {8, 9, 10, 11}

    • 17 circuits of size 5:

      {3, 4, 5, 6, 7}, {5, 6, 7, 8, 9}, {5, 6, 7, 8, 10}, {3, 4, 5, 9, 10}, {5, 6, 7, 9, 10}, {5, 6, 8, 9, 10}, {5, 7, 8, 9, 10}, {6, 7, 8, 9, 10}, {5, 6, 7, 9, 11}, {5, 6, 8, 9, 11}, {5, 7, 8, 9, 11}, {5, 6, 7, 10, 11}, {5, 6, 8, 10, 11}, {5, 7, 8, 10, 11}, {5, 6, 9, 10, 11}, {5, 7, 9, 10, 11}, {6, 7, 9, 10, 11}

    • 37 circuits of size 6:

      {0, 1, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {3, 4, 5, 6, 8, 9}, {3, 4, 5, 7, 8, 9}, {3, 4, 6, 7, 8, 9}, {3, 4, 5, 6, 8, 10}, {3, 4, 5, 7, 8, 10}, {3, 4, 6, 7, 8, 10}, {0, 1, 3, 5, 9, 10}, {0, 2, 3, 5, 9, 10}, {1, 2, 3, 5, 9, 10}, {0, 1, 4, 5, 9, 10}, {0, 2, 4, 5, 9, 10}, {1, 2, 4, 5, 9, 10}, {3, 4, 6, 7, 9, 10}, {3, 4, 6, 8, 9, 10}, {3, 4, 7, 8, 9, 10}, {3, 4, 5, 6, 8, 11}, {3, 4, 5, 7, 8, 11}, {3, 4, 5, 6, 9, 11}, {3, 4, 5, 7, 9, 11}, {3, 4, 6, 7, 9, 11}, {3, 4, 5, 8, 9, 11}, {3, 4, 6, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {3, 4, 5, 6, 10, 11}, {3, 4, 5, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {3, 4, 5, 8, 10, 11}, {3, 4, 6, 8, 10, 11}, {3, 4, 7, 8, 10, 11}, {3, 4, 6, 9, 10, 11}, {3, 4, 7, 9, 10, 11}

    • 150 circuits of size 7:

      {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {1, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {1, 2, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {1, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 1, 4, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 3, 7, 8, 9, 11}, {1, 2, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 4, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {1, 2, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 2, 3, 7, 9, 10, 11}, {1, 2, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}

---

---

10. Graph1210:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,0}, {0,7}, {7,8}, {2,7}, {1,8}, {8,9}, {9,10}, {9,11}, {4,10}, {6,10}, {3,11}, {5,11}

• Randomly generated (generic) hyperplane:

  51*a + 12*b + 19*c + 59*d + 3*e + 86*f + 83*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 0 : 1 : 0 : -3/83]

  [0 : 0 : 1 : 0 : -19/3 : 0 : 0]

  [0 : 0 : 1 : 19/113 : -19/113 : -19/113 : -19/113]

  [1 : 0 : 0 : -38/113 : -75/113 : -75/113 : 38/113]

  [1 : 25/4 : 0 : 21/4 : 0 : 0 : -21/4]

  [1 : 32/95 : 0 : 0 : 0 : 0 : -63/95]

  [0 : 1 : 0 : 0 : 0 : 0 : -12/83]

  [0 : 0 : 1 : 1 : -87/40 : -1 : 7/40]

  [0 : 0 : 1 : 8/15 : -23/15 : -8/15 : 0]

  [0 : 0 : 0 : 1 : 4 : 4 : -5]

  [0 : 1 : 0 : 1/2 : 0 : 0 : -1/2]

  [1 : 0 : 0 : 0 : 16/3 : 16/3 : -19/3]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 660 bases, 264 non-bases

  • circuits:

    • 7 circuits of size 4:

      {0, 1, 2, 7}, {0, 1, 2, 8}, {0, 1, 7, 8}, {0, 2, 7, 8}, {1, 2, 7, 8}, {4, 5, 6, 10}, {3, 4, 5, 11}

    • 15 circuits of size 5:

      {3, 4, 5, 6, 9}, {3, 4, 5, 9, 10}, {3, 4, 6, 9, 10}, {3, 5, 6, 9, 10}, {3, 4, 6, 9, 11}, {3, 5, 6, 9, 11}, {4, 5, 6, 9, 11}, {3, 4, 6, 10, 11}, {3, 5, 6, 10, 11}, {3, 4, 9, 10, 11}, {3, 5, 9, 10, 11}, {4, 5, 9, 10, 11}, {3, 6, 9, 10, 11}, {4, 6, 9, 10, 11}, {5, 6, 9, 10, 11}

    • 20 circuits of size 6:

      {0, 1, 2, 6, 9, 10}, {0, 1, 6, 7, 9, 10}, {0, 2, 6, 7, 9, 10}, {1, 2, 6, 7, 9, 10}, {0, 1, 6, 8, 9, 10}, {0, 2, 6, 8, 9, 10}, {1, 2, 6, 8, 9, 10}, {0, 6, 7, 8, 9, 10}, {1, 6, 7, 8, 9, 10}, {2, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 9, 11}, {0, 1, 3, 7, 9, 11}, {0, 2, 3, 7, 9, 11}, {1, 2, 3, 7, 9, 11}, {0, 1, 3, 8, 9, 11}, {0, 2, 3, 8, 9, 11}, {1, 2, 3, 8, 9, 11}, {0, 3, 7, 8, 9, 11}, {1, 3, 7, 8, 9, 11}, {2, 3, 7, 8, 9, 11}

    • 250 circuits of size 7:

      {0, 1, 2, 3, 4, 5, 6}, {0, 1, 3, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 3, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 5, 9}, {0, 1, 2, 3, 4, 6, 9}, {0, 1, 2, 3, 5, 6, 9}, {0, 1, 2, 4, 5, 6, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {1, 2, 3, 4, 5, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 4, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {0, 4, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 5, 10}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 1, 3, 5, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 4, 9, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 2, 3, 4, 8, 9, 10}, {1, 2, 3, 4, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {2, 3, 4, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 1, 2, 4, 5, 6, 11}, {0, 1, 3, 4, 6, 7, 11}, {0, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 1, 3, 5, 6, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 4, 5, 6, 7, 11}, {0, 2, 4, 5, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 1, 4, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 4, 5, 6, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 4, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {0, 5, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 4, 10, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 5, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {2, 3, 4, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {0, 4, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {0, 4, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {0, 5, 6, 7, 8, 10, 11}, {1, 5, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {1, 2, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {2, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}

---

---

11. Graph1211:

• Edges of graph:

  {0,1}, {0,2}, {1,3}, {1,4}, {2,3}, {4,2}, {3,6}, {6,5}, {5,4}, {7,6}, {5,8}, {8,9}, {8,10}, {10,7}, {7,9}, {9,11}, {10,11}, {0,11}

• Randomly generated (generic) hyperplane:

  50*a + 95*b + 40*c + 52*d + 14*e + 28*f + 34*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : -25/47 : -25/47 : -25/47 : 0]

  [1 : 0 : 0 : 0 : 0 : -25/14 : 0]

  [1 : 44/29 : 0 : -73/29 : -73/29 : -1 : 0]

  [1 : -1 : 0 : 0 : 0 : 45/28 : 0]

  [1 : -22/29 : 0 : 22/29 : 22/29 : -1 : 0]

  [1 : -1 : 1/24 : 25/24 : 25/24 : -23/24 : 1/24]

  [1 : -1 : 101/74 : 0 : 0 : -2 : 101/74]

  [0 : 0 : 1 : -37/26 : 0 : 0 : 1]

  [0 : 0 : 1 : -5/16 : -5/16 : -5/16 : -5/16]

  [0 : 0 : 1 : -20/9 : 0 : 0 : 20/9]

  [0 : 0 : 0 : 1 : -13/19 : -13/19 : -13/19]

  [0 : 0 : 0 : 1 : -9/38 : -9/38 : -47/38]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 600 bases, 324 non-bases

  • circuits:

    • 10 circuits of size 4:

      {0, 1, 2, 3}, {0, 1, 2, 4}, {0, 1, 3, 4}, {0, 2, 3, 4}, {1, 2, 3, 4}, {7, 8, 9, 10}, {7, 8, 9, 11}, {7, 8, 10, 11}, {7, 9, 10, 11}, {8, 9, 10, 11}

    • 20 circuits of size 5:

      {0, 1, 2, 5, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 5, 6}, {1, 2, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 4, 5, 6}, {1, 2, 4, 5, 6}, {0, 3, 4, 5, 6}, {1, 3, 4, 5, 6}, {2, 3, 4, 5, 6}, {5, 6, 7, 8, 9}, {5, 6, 7, 8, 10}, {5, 6, 7, 9, 10}, {5, 6, 8, 9, 10}, {5, 6, 7, 8, 11}, {5, 6, 7, 9, 11}, {5, 6, 8, 9, 11}, {5, 6, 7, 10, 11}, {5, 6, 8, 10, 11}, {5, 6, 9, 10, 11}

    • 200 circuits of size 7:

      {0, 1, 2, 5, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 1, 2, 6, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {1, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {0, 1, 2, 5, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 1, 2, 6, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {1, 2, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {2, 3, 4, 5, 7, 9, 10}, {0, 1, 2, 6, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {2, 3, 4, 5, 8, 9, 10}, {0, 1, 2, 6, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {0, 1, 2, 5, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 1, 2, 6, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {2, 3, 4, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 3, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {2, 3, 4, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {2, 3, 4, 6, 7, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 3, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {2, 3, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {0, 3, 4, 5, 9, 10, 11}, {1, 3, 4, 5, 9, 10, 11}, {2, 3, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {2, 3, 4, 6, 9, 10, 11}

---

---

12. Graph1212:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,0}, {0,7}, {7,1}, {2,10}, {10,8}, {8,7}, {3,10}, {8,9}, {9,11}, {11,4}, {5,11}, {9,6}

• Randomly generated (generic) hyperplane:

  26*a + 79*b + 35*c + 53*d + 42*e + 42*f + 56*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : -11/7 : 0 : -4/7 : 0 : 0]

  [0 : 1 : -3/2 : -1/2 : 0 : 0 : 0]

  [1 : 5/22 : 0 : 5/22 : 0 : 0 : -1]

  [1 : 30/23 : 0 : 0 : 0 : 0 : -53/23]

  [0 : 1 : 0 : 0 : 0 : -23/98 : -121/98]

  [0 : 1 : 0 : 0 : 121/56 : -65/56 : -121/56]

  [0 : 1 : 0 : 0 : 1 : 0 : -121/56]

  [0 : 0 : 1 : -7 : 8 : 0 : 0]

  [0 : 0 : 0 : 1 : -109/98 : 0 : -11/98]

  [0 : 0 : 0 : 0 : 1 : 0 : -3/4]

  [1 : -1 : 0 : 53/109 : 0 : 0 : 53/109]

  [0 : 0 : 0 : 0 : 1 : -3/7 : -3/7]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 486 bases, 438 non-bases

  • circuits:

    • 3 circuits of size 3:

      {0, 1, 7}, {2, 3, 10}, {4, 5, 11}

    • 3 circuits of size 4:

      {4, 5, 6, 9}, {4, 6, 9, 11}, {5, 6, 9, 11}

    • 15 circuits of size 5:

      {0, 1, 2, 3, 8}, {0, 2, 3, 7, 8}, {1, 2, 3, 7, 8}, {0, 1, 6, 8, 9}, {2, 3, 6, 8, 9}, {0, 6, 7, 8, 9}, {1, 6, 7, 8, 9}, {0, 1, 2, 8, 10}, {0, 1, 3, 8, 10}, {0, 2, 7, 8, 10}, {1, 2, 7, 8, 10}, {0, 3, 7, 8, 10}, {1, 3, 7, 8, 10}, {2, 6, 8, 9, 10}, {3, 6, 8, 9, 10}

    • 45 circuits of size 6:

      {0, 1, 4, 5, 6, 8}, {2, 3, 4, 5, 6, 8}, {0, 4, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 6, 9}, {0, 2, 3, 6, 7, 9}, {1, 2, 3, 6, 7, 9}, {0, 1, 4, 5, 8, 9}, {2, 3, 4, 5, 8, 9}, {0, 4, 5, 7, 8, 9}, {1, 4, 5, 7, 8, 9}, {2, 4, 5, 6, 8, 10}, {3, 4, 5, 6, 8, 10}, {0, 1, 2, 6, 9, 10}, {0, 1, 3, 6, 9, 10}, {0, 2, 6, 7, 9, 10}, {1, 2, 6, 7, 9, 10}, {0, 3, 6, 7, 9, 10}, {1, 3, 6, 7, 9, 10}, {2, 4, 5, 8, 9, 10}, {3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 11}, {2, 3, 4, 6, 8, 11}, {0, 1, 5, 6, 8, 11}, {2, 3, 5, 6, 8, 11}, {0, 4, 6, 7, 8, 11}, {1, 4, 6, 7, 8, 11}, {0, 5, 6, 7, 8, 11}, {1, 5, 6, 7, 8, 11}, {0, 1, 4, 8, 9, 11}, {2, 3, 4, 8, 9, 11}, {0, 1, 5, 8, 9, 11}, {2, 3, 5, 8, 9, 11}, {0, 4, 7, 8, 9, 11}, {1, 4, 7, 8, 9, 11}, {0, 5, 7, 8, 9, 11}, {1, 5, 7, 8, 9, 11}, {2, 4, 6, 8, 10, 11}, {3, 4, 6, 8, 10, 11}, {2, 5, 6, 8, 10, 11}, {3, 5, 6, 8, 10, 11}, {2, 4, 8, 9, 10, 11}, {3, 4, 8, 9, 10, 11}, {2, 5, 8, 9, 10, 11}, {3, 5, 8, 9, 10, 11}

    • 54 circuits of size 7:

      {0, 1, 2, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 4, 5, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 4, 5, 6, 10}, {0, 1, 3, 4, 5, 6, 10}, {0, 2, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 3, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 2, 3, 4, 9, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 3, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}

---

---

13. Graph1213:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {1,6}, {2,6}, {6,7}, {7,8}, {8,3}, {8,9}, {7,9}, {9,10}, {5,10}, {10,11}, {11,0}, {4,11}

• Randomly generated (generic) hyperplane:

  34*a + 49*b + 22*c + 11*d + 83*e + 87*f + 17*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 1 : 0 : -2/5 : 7/5]

  [1 : 0 : 0 : -17/14 : 0 : 0 : -17/14]

  [1 : -34/125 : 0 : 34/125 : 0 : -34/125 : 0]

  [1 : 1 : 0 : -1 : 0 : 1 : -159/17]

  [0 : 0 : 0 : 0 : 1 : 1 : -10]

  [0 : 0 : 0 : 1 : -49/85 : 36/85 : 0]

  [1 : -6/125 : 0 : -119/125 : 0 : -6/125 : -1]

  [1 : 1 : -131/11 : 109/11 : 0 : 1 : -1]

  [1 : 1 : -71/11 : -1 : 0 : 1 : -1]

  [0 : 0 : 1 : -2 : 0 : 0 : 0]

  [0 : 0 : 0 : 1 : -11/83 : 0 : 0]

  [0 : 0 : 0 : 0 : 1 : -83/70 : 83/70]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 540 bases, 384 non-bases

  • circuits:

    • 2 circuits of size 3:

      {1, 2, 6}, {7, 8, 9}

    • 5 circuits of size 4:

      {0, 4, 5, 10}, {0, 4, 5, 11}, {0, 4, 10, 11}, {0, 5, 10, 11}, {4, 5, 10, 11}

    • 9 circuits of size 5:

      {1, 2, 3, 7, 8}, {1, 3, 6, 7, 8}, {2, 3, 6, 7, 8}, {1, 2, 3, 7, 9}, {1, 3, 6, 7, 9}, {2, 3, 6, 7, 9}, {1, 2, 3, 8, 9}, {1, 3, 6, 8, 9}, {2, 3, 6, 8, 9}

    • 60 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 6}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 5, 7, 9}, {0, 3, 4, 5, 8, 9}, {0, 1, 2, 3, 4, 10}, {0, 1, 2, 3, 5, 10}, {1, 2, 3, 4, 5, 10}, {0, 1, 3, 4, 6, 10}, {0, 2, 3, 4, 6, 10}, {0, 1, 3, 5, 6, 10}, {0, 2, 3, 5, 6, 10}, {1, 3, 4, 5, 6, 10}, {2, 3, 4, 5, 6, 10}, {0, 3, 4, 7, 8, 10}, {0, 3, 5, 7, 8, 10}, {3, 4, 5, 7, 8, 10}, {0, 3, 4, 7, 9, 10}, {0, 3, 5, 7, 9, 10}, {3, 4, 5, 7, 9, 10}, {0, 3, 4, 8, 9, 10}, {0, 3, 5, 8, 9, 10}, {3, 4, 5, 8, 9, 10}, {0, 1, 2, 3, 4, 11}, {0, 1, 2, 3, 5, 11}, {1, 2, 3, 4, 5, 11}, {0, 1, 3, 4, 6, 11}, {0, 2, 3, 4, 6, 11}, {0, 1, 3, 5, 6, 11}, {0, 2, 3, 5, 6, 11}, {1, 3, 4, 5, 6, 11}, {2, 3, 4, 5, 6, 11}, {0, 3, 4, 7, 8, 11}, {0, 3, 5, 7, 8, 11}, {3, 4, 5, 7, 8, 11}, {0, 3, 4, 7, 9, 11}, {0, 3, 5, 7, 9, 11}, {3, 4, 5, 7, 9, 11}, {0, 3, 4, 8, 9, 11}, {0, 3, 5, 8, 9, 11}, {3, 4, 5, 8, 9, 11}, {0, 1, 2, 3, 10, 11}, {1, 2, 3, 4, 10, 11}, {1, 2, 3, 5, 10, 11}, {0, 1, 3, 6, 10, 11}, {0, 2, 3, 6, 10, 11}, {1, 3, 4, 6, 10, 11}, {2, 3, 4, 6, 10, 11}, {1, 3, 5, 6, 10, 11}, {2, 3, 5, 6, 10, 11}, {0, 3, 7, 8, 10, 11}, {3, 4, 7, 8, 10, 11}, {3, 5, 7, 8, 10, 11}, {0, 3, 7, 9, 10, 11}, {3, 4, 7, 9, 10, 11}, {3, 5, 7, 9, 10, 11}, {0, 3, 8, 9, 10, 11}, {3, 4, 8, 9, 10, 11}, {3, 5, 8, 9, 10, 11}

    • 90 circuits of size 7:

      {0, 1, 2, 4, 5, 7, 8}, {0, 1, 4, 5, 6, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 2, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {0, 1, 5, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 2, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {0, 1, 5, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {0, 1, 2, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 1, 6, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {1, 5, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {0, 1, 2, 8, 9, 10, 11}, {1, 2, 4, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}

---

---

14. Graph1214:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,1}, {4,5}, {5,6}, {6,7}, {7,8}, {8,3}, {6,11}, {11,10}, {9,10}, {9,7}, {8,9}, {11,5}, {0,10}

• Randomly generated (generic) hyperplane:

  84*a + 16*b + 39*c + 14*d + 6*e + 95*f + 50*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : 0 : 0 : -84/95 : 0]

  [1 : 179/79 : 0 : 0 : 0 : -100/79 : 0]

  [1 : -21/4 : 0 : 0 : 0 : 0 : 0]

  [0 : 1 : 0 : 16/31 : 0 : -16/31 : 16/31]

  [0 : 1 : 0 : 79/64 : 0 : -1 : 79/64]

  [0 : 0 : 1 : 11/64 : 0 : 0 : -53/64]

  [0 : 0 : 1 : -34/19 : 0 : 53/19 : -106/19]

  [0 : 0 : 0 : 1 : -19/56 : -1 : 93/56]

  [0 : 0 : 0 : 1 : 31/56 : -1 : 87/56]

  [0 : 0 : 0 : 1 : -1 : -1 : 87/50]

  [0 : 0 : 0 : 0 : 0 : 1 : -19/10]

  [0 : 0 : 1 : 0 : 0 : 11/45 : -56/45]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 486 bases, 438 non-bases

  • circuits:

    • 3 circuits of size 3:

      {0, 1, 2}, {7, 8, 9}, {5, 6, 11}

    • 3 circuits of size 4:

      {0, 1, 3, 4}, {0, 2, 3, 4}, {1, 2, 3, 4}

    • 15 circuits of size 5:

      {3, 4, 5, 6, 10}, {3, 4, 7, 8, 10}, {5, 6, 7, 8, 10}, {3, 4, 7, 9, 10}, {5, 6, 7, 9, 10}, {3, 4, 8, 9, 10}, {5, 6, 8, 9, 10}, {3, 4, 5, 10, 11}, {3, 4, 6, 10, 11}, {5, 7, 8, 10, 11}, {6, 7, 8, 10, 11}, {5, 7, 9, 10, 11}, {6, 7, 9, 10, 11}, {5, 8, 9, 10, 11}, {6, 8, 9, 10, 11}

    • 45 circuits of size 6:

      {3, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 9}, {3, 4, 5, 6, 8, 9}, {0, 1, 3, 5, 6, 10}, {0, 2, 3, 5, 6, 10}, {1, 2, 3, 5, 6, 10}, {0, 1, 4, 5, 6, 10}, {0, 2, 4, 5, 6, 10}, {1, 2, 4, 5, 6, 10}, {0, 1, 3, 7, 8, 10}, {0, 2, 3, 7, 8, 10}, {1, 2, 3, 7, 8, 10}, {0, 1, 4, 7, 8, 10}, {0, 2, 4, 7, 8, 10}, {1, 2, 4, 7, 8, 10}, {0, 1, 3, 7, 9, 10}, {0, 2, 3, 7, 9, 10}, {1, 2, 3, 7, 9, 10}, {0, 1, 4, 7, 9, 10}, {0, 2, 4, 7, 9, 10}, {1, 2, 4, 7, 9, 10}, {0, 1, 3, 8, 9, 10}, {0, 2, 3, 8, 9, 10}, {1, 2, 3, 8, 9, 10}, {0, 1, 4, 8, 9, 10}, {0, 2, 4, 8, 9, 10}, {1, 2, 4, 8, 9, 10}, {3, 4, 5, 7, 8, 11}, {3, 4, 6, 7, 8, 11}, {3, 4, 5, 7, 9, 11}, {3, 4, 6, 7, 9, 11}, {3, 4, 5, 8, 9, 11}, {3, 4, 6, 8, 9, 11}, {0, 1, 3, 5, 10, 11}, {0, 2, 3, 5, 10, 11}, {1, 2, 3, 5, 10, 11}, {0, 1, 4, 5, 10, 11}, {0, 2, 4, 5, 10, 11}, {1, 2, 4, 5, 10, 11}, {0, 1, 3, 6, 10, 11}, {0, 2, 3, 6, 10, 11}, {1, 2, 3, 6, 10, 11}, {0, 1, 4, 6, 10, 11}, {0, 2, 4, 6, 10, 11}, {1, 2, 4, 6, 10, 11}

    • 54 circuits of size 7:

      {0, 1, 3, 5, 6, 7, 8}, {0, 2, 3, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 7, 8}, {0, 1, 4, 5, 6, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}

---

---

15. Graph1215:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {5,6}, {6,7}, {7,8}, {8,5}, {0,5}, {1,6}, {4,8}, {7,9}, {9,10}, {10,11}, {11,9}, {10,2}, {11,3}

• Randomly generated (generic) hyperplane:

  98*a + 65*b + 24*c + 17*d + 62*e + 21*f + 91*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : -41/12 : 1 : 0 : 0 : 0]

  [1 : 0 : -19/24 : -1 : -1 : 0 : 0]

  [1 : 0 : 77/34 : -77/34 : -77/34 : 43/34 : 0]

  [1 : 0 : 0 : 0 : 0 : -14/3 : 0]

  [1 : -49/41 : 0 : -49/41 : 0 : 0 : 0]

  [0 : 1 : 10/19 : 1 : -29/19 : 0 : 0]

  [1 : 0 : 1/2 : -1 : -3/2 : 0 : 0]

  [1 : 0 : 36/55 : -36/55 : -91/55 : 0 : 0]

  [1 : -9/5 : 0 : -9/5 : 4/5 : 0 : 0]

  [0 : 0 : 1 : -1 : -1 : 0 : 55/91]

  [0 : 0 : 1 : -1 : -1 : 73/56 : 17/56]

  [0 : 0 : 0 : 0 : 0 : 1 : -3/13]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 576 bases, 348 non-bases

  • circuits:

    • 1 circuit of size 3:

      {9, 10, 11}

    • 6 circuits of size 4:

      {0, 1, 5, 6}, {0, 4, 5, 8}, {5, 6, 7, 8}, {2, 3, 9, 10}, {2, 3, 9, 11}, {2, 3, 10, 11}

    • 15 circuits of size 5:

      {0, 1, 2, 3, 4}, {0, 1, 4, 5, 7}, {1, 2, 3, 6, 7}, {0, 1, 4, 6, 7}, {0, 4, 5, 6, 7}, {1, 4, 5, 6, 7}, {0, 1, 4, 6, 8}, {1, 4, 5, 6, 8}, {0, 1, 4, 7, 8}, {2, 3, 4, 7, 8}, {0, 1, 5, 7, 8}, {1, 4, 5, 7, 8}, {0, 1, 6, 7, 8}, {0, 4, 6, 7, 8}, {1, 4, 6, 7, 8}

    • 38 circuits of size 6:

      {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 5, 8}, {1, 2, 3, 4, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 6, 8}, {2, 3, 4, 5, 6, 8}, {0, 1, 2, 3, 7, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 1, 2, 4, 9, 10}, {0, 1, 3, 4, 9, 10}, {1, 2, 6, 7, 9, 10}, {1, 3, 6, 7, 9, 10}, {2, 4, 7, 8, 9, 10}, {3, 4, 7, 8, 9, 10}, {0, 1, 2, 4, 9, 11}, {0, 1, 3, 4, 9, 11}, {1, 2, 6, 7, 9, 11}, {1, 3, 6, 7, 9, 11}, {2, 4, 7, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {0, 1, 2, 4, 10, 11}, {0, 1, 3, 4, 10, 11}, {1, 2, 6, 7, 10, 11}, {1, 3, 6, 7, 10, 11}, {2, 4, 7, 8, 10, 11}, {3, 4, 7, 8, 10, 11}

    • 120 circuits of size 7:

      {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {3, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {0, 1, 2, 6, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {3, 4, 5, 6, 8, 9, 10}, {0, 1, 2, 7, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {3, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {3, 4, 5, 6, 8, 9, 11}, {0, 1, 2, 7, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {0, 2, 6, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {0, 3, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 3, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {3, 4, 5, 6, 7, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {3, 4, 5, 6, 8, 10, 11}, {0, 1, 2, 7, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}

---

---

16. Graph1216:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,0}, {1,6}, {5,2}, {3,4}, {4,5}, {6,5}, {4,8}, {7,6}, {8,9}, {8,10}, {10,7}, {7,9}, {10,11}, {9,11}, {0,11}

• Randomly generated (generic) hyperplane:

  86*a + 28*b + 60*c + 73*d + 16*e + 51*f + 43*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 0 : 0 : -5/9 : 0 : -4/9]

  [1 : 14/3 : 0 : 0 : -1 : 0 : -14/3]

  [ 1: 0 : -35/38 : 0 : -73/38 : 0 : 0]

  [0 : 1 : -3/19 : 0 : -22/19 : 0 : 0]

  [0 : 1 : -7/15 : 0 : 0 : 0 : 0]

  [1 : -73/14 : 1 : 0 : 0 : 0 : 0]

  [1 : -1 : -85/33 : 0 : -118/33 : 0 : 118/33]

  [0 : 0 : 1 : -33/73 : 1 : 0 : -1]

  [0 : 0 : 1 : -60/49 : 60/49 : 60/49 : -60/49]

  [0 : 0 : 1 : -1 : 1 : 40/51 : -1]

  [0 : 0 : 0 : 1 : -73/24 : -73/24 : 73/24]

  [0 : 0 : 0 : 0 : 1 : 9/17 : -1]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 640 bases, 284 non-bases

  • circuits:

    • 8 circuits of size 4:

      {0, 1, 2, 3}, {2, 3, 4, 5}, {1, 2, 5, 6}, {7, 8, 9, 10}, {7, 8, 9, 11}, {7, 8, 10, 11}, {7, 9, 10, 11}, {8, 9, 10, 11}

    • 12 circuits of size 5:

      {0, 1, 2, 4, 5}, {0, 1, 3, 4, 5}, {0, 1, 2, 4, 6}, {0, 1, 3, 4, 6}, {0, 2, 3, 4, 6}, {1, 2, 3, 4, 6}, {0, 1, 3, 5, 6}, {0, 2, 3, 5, 6}, {0, 1, 4, 5, 6}, {0, 2, 4, 5, 6}, {0, 3, 4, 5, 6}, {1, 3, 4, 5, 6}

    • 30 circuits of size 6:

      {0, 3, 4, 7, 8, 9}, {0, 1, 6, 7, 8, 9}, {4, 5, 6, 7, 8, 9}, {0, 3, 4, 7, 8, 10}, {0, 1, 6, 7, 8, 10}, {4, 5, 6, 7, 8, 10}, {0, 3, 4, 7, 9, 10}, {0, 1, 6, 7, 9, 10}, {4, 5, 6, 7, 9, 10}, {0, 3, 4, 8, 9, 10}, {0, 1, 6, 8, 9, 10}, {4, 5, 6, 8, 9, 10}, {0, 3, 4, 7, 8, 11}, {0, 1, 6, 7, 8, 11}, {4, 5, 6, 7, 8, 11}, {0, 3, 4, 7, 9, 11}, {0, 1, 6, 7, 9, 11}, {4, 5, 6, 7, 9, 11}, {0, 3, 4, 8, 9, 11}, {0, 1, 6, 8, 9, 11}, {4, 5, 6, 8, 9, 11}, {0, 3, 4, 7, 10, 11}, {0, 1, 6, 7, 10, 11}, {4, 5, 6, 7, 10, 11}, {0, 3, 4, 8, 10, 11}, {0, 1, 6, 8, 10, 11}, {4, 5, 6, 8, 10, 11}, {0, 3, 4, 9, 10, 11}, {0, 1, 6, 9, 10, 11}, {4, 5, 6, 9, 10, 11}

    • 200 circuits of size 7:

      {0, 1, 2, 4, 7, 8, 9}, {1, 2, 3, 4, 7, 8, 9}, {0, 1, 2, 5, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {1, 2, 3, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {0, 1, 2, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 2, 5, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {1, 2, 3, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {1, 2, 3, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {0, 1, 2, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 2, 5, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {1, 2, 3, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {0, 1, 2, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {2, 3, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {1, 2, 3, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {1, 3, 4, 5, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {2, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}

---

---

17. Graph1217:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {4,5}, {5,6}, {6,7}, {7,3}, {1,8}, {8,2}, {8,9}, {9,10}, {7,10}, {11,6}, {10,11}, {5,11}, {0,9}

• Randomly generated (generic) hyperplane:

  19*a + 98*b + 70*c + 92*d + 66*e + 71*f + 63*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 49/11 : -49/11 : 0 : 0 : 0]

  [1 : 1 : 117/22 : -117/22 : 0 : 0 : 0]

  [1 : -37/2 : 0 : 39/2 : 0 : 0 : 0]

  [0 : 1 : 0 : -161/155 : 0 : 0 : -6/155]

  [0 : 1 : 0 : 0 : 0 : 0 : -14/9]

  [0 : 0 : 0 : 0 : 1 : 1 : -137/63]

  [0 : 0 : 0 : 0 : 1 : -129/8 : 137/8]

  [0 : 0 : 0 : 1 : -155/129 : 0 : -26/129]

  [1 : -111/28 : 111/28 : 1 : 0 : 0 : 0]

  [0 : 1 : -1 : -7/23 : 0 : 0 : 0]

  [0 : 0 : 0 : 1 : -46/33 : 0 : 0]

  [0 : 0 : 0 : 0 : 1 : -33/4 : 33/4]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 486 bases, 438 non-bases

  • circuits:

    • 2 circuits of size 3:

      {1, 2, 8}, {5, 6, 11}

    • 8 circuits of size 4:

      {0, 1, 2, 9}, {0, 3, 4, 9}, {0, 1, 8, 9}, {0, 2, 8, 9}, {3, 4, 7, 10}, {5, 6, 7, 10}, {5, 7, 10, 11}, {6, 7, 10, 11}

    • 14 circuits of size 5:

      {0, 1, 2, 3, 4}, {3, 4, 5, 6, 7}, {0, 1, 3, 4, 8}, {0, 2, 3, 4, 8}, {1, 2, 3, 4, 9}, {1, 3, 4, 8, 9}, {2, 3, 4, 8, 9}, {3, 4, 5, 6, 10}, {0, 3, 7, 9, 10}, {0, 4, 7, 9, 10}, {3, 4, 5, 7, 11}, {3, 4, 6, 7, 11}, {3, 4, 5, 10, 11}, {3, 4, 6, 10, 11}

    • 24 circuits of size 6:

      {0, 3, 5, 6, 7, 9}, {0, 4, 5, 6, 7, 9}, {0, 1, 2, 3, 7, 10}, {0, 1, 2, 4, 7, 10}, {0, 1, 3, 7, 8, 10}, {0, 2, 3, 7, 8, 10}, {0, 1, 4, 7, 8, 10}, {0, 2, 4, 7, 8, 10}, {0, 3, 5, 6, 9, 10}, {0, 4, 5, 6, 9, 10}, {1, 2, 3, 7, 9, 10}, {1, 2, 4, 7, 9, 10}, {1, 3, 7, 8, 9, 10}, {2, 3, 7, 8, 9, 10}, {1, 4, 7, 8, 9, 10}, {2, 4, 7, 8, 9, 10}, {0, 3, 5, 7, 9, 11}, {0, 4, 5, 7, 9, 11}, {0, 3, 6, 7, 9, 11}, {0, 4, 6, 7, 9, 11}, {0, 3, 5, 9, 10, 11}, {0, 4, 5, 9, 10, 11}, {0, 3, 6, 9, 10, 11}, {0, 4, 6, 9, 10, 11}

    • 72 circuits of size 7:

      {0, 1, 2, 3, 5, 6, 7}, {0, 1, 2, 4, 5, 6, 7}, {0, 1, 3, 5, 6, 7, 8}, {0, 2, 3, 5, 6, 7, 8}, {0, 1, 4, 5, 6, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 5, 6, 10}, {0, 1, 2, 4, 5, 6, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {0, 1, 2, 3, 5, 7, 11}, {0, 1, 2, 4, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {0, 1, 2, 4, 6, 7, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 3, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {2, 3, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {2, 4, 5, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {2, 3, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}

---

---

18. Graph1218:

• Edges of graph:

  {0,1}, {1,6}, {6,0}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {4,11}, {7,11}, {3,7}, {5,10}, {8,2}, {7,8}, {8,9}, {10,9}, {10,11}, {0,9}

• Randomly generated (generic) hyperplane:

  5*a + 61*b + 17*c + 82*d + 80*e + 28*f + 51*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 1 : 0 : -1 : 9/4 : 0]

  [0 : 1 : 0 : 0 : 0 : -61/28 : 0]

  [0 : 1 : -61/16 : 0 : 61/16 : -61/16 : -61/16]

  [0 : 0 : 1 : 0 : -17 : 17 : 17]

  [1 : 0 : -36/17 : 1 : 0 : 0 : -1]

  [1 : -53/96 : 149/96 : 1 : -53/96 : 53/96 : -1]

  [0 : 1 : 11/21 : 0 : -11/21 : -1 : 0]

  [0 : 1 : -1 : 1 : -126 : 126 : 126]

  [0 : 1 : -1 : -45/83 : 38/83 : -38/83 : -38/83]

  [0 : 0 : 1 : 35/83 : -48/83 : 48/83 : -35/83]

  [1 : -1 : 139/48 : 91/48 : -1 : 1 : -91/48]

  [1 : -36/127 : 36/127 : 91/127 : -36/127 : 36/127 : -91/127]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 630 bases, 294 non-bases

  • circuits:

    • 1 circuit of size 3:

      {0, 1, 6}

    • 3 circuits of size 4:

      {2, 3, 7, 8}, {3, 4, 7, 11}, {4, 5, 10, 11}

    • 12 circuits of size 5:

      {0, 1, 2, 8, 9}, {0, 2, 6, 8, 9}, {1, 2, 6, 8, 9}, {3, 4, 5, 7, 10}, {0, 1, 5, 9, 10}, {0, 5, 6, 9, 10}, {1, 5, 6, 9, 10}, {2, 5, 8, 9, 10}, {2, 3, 4, 8, 11}, {2, 4, 7, 8, 11}, {3, 5, 7, 10, 11}, {7, 8, 9, 10, 11}

    • 54 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 7, 9}, {2, 3, 4, 5, 7, 9}, {0, 2, 3, 6, 7, 9}, {1, 2, 3, 6, 7, 9}, {2, 3, 4, 5, 8, 9}, {0, 1, 3, 7, 8, 9}, {2, 4, 5, 7, 8, 9}, {3, 4, 5, 7, 8, 9}, {0, 3, 6, 7, 8, 9}, {1, 3, 6, 7, 8, 9}, {0, 1, 2, 5, 8, 10}, {2, 3, 4, 5, 8, 10}, {0, 2, 5, 6, 8, 10}, {1, 2, 5, 6, 8, 10}, {2, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 9, 10}, {2, 3, 4, 7, 9, 10}, {2, 3, 5, 7, 9, 10}, {2, 4, 5, 7, 9, 10}, {2, 3, 4, 8, 9, 10}, {3, 4, 5, 8, 9, 10}, {2, 4, 7, 8, 9, 10}, {3, 4, 7, 8, 9, 10}, {3, 5, 7, 8, 9, 10}, {4, 5, 7, 8, 9, 10}, {0, 1, 4, 5, 9, 11}, {2, 3, 4, 5, 9, 11}, {0, 4, 5, 6, 9, 11}, {1, 4, 5, 6, 9, 11}, {2, 3, 5, 7, 9, 11}, {2, 4, 5, 7, 9, 11}, {2, 3, 5, 8, 9, 11}, {2, 4, 5, 8, 9, 11}, {3, 4, 5, 8, 9, 11}, {2, 5, 7, 8, 9, 11}, {3, 5, 7, 8, 9, 11}, {4, 5, 7, 8, 9, 11}, {2, 3, 5, 8, 10, 11}, {2, 5, 7, 8, 10, 11}, {0, 1, 4, 9, 10, 11}, {2, 3, 4, 9, 10, 11}, {2, 3, 5, 9, 10, 11}, {0, 4, 6, 9, 10, 11}, {1, 4, 6, 9, 10, 11}, {2, 3, 7, 9, 10, 11}, {2, 4, 7, 9, 10, 11}, {2, 5, 7, 9, 10, 11}, {2, 3, 8, 9, 10, 11}, {2, 4, 8, 9, 10, 11}, {3, 4, 8, 9, 10, 11}, {3, 5, 8, 9, 10, 11}

    • 162 circuits of size 7:

      {0, 1, 2, 4, 5, 7, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 3, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 4, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 7, 10}, {0, 1, 2, 3, 5, 7, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 4, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {0, 4, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 4, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 5, 7, 11}, {0, 1, 2, 4, 5, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 2, 4, 5, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 5, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {0, 4, 5, 6, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 4, 9, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {0, 5, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 4, 10, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 2, 3, 7, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 1, 2, 3, 8, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {0, 1, 2, 7, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {0, 4, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {0, 5, 6, 7, 8, 10, 11}, {1, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 3, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {0, 1, 3, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}

---

---

19. Graph1219:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {7,8}, {8,9}, {9,10}, {10,11}, {11,7}, {0,6}, {6,5}, {6,7}, {1,8}, {2,9}, {3,11}, {4,10}

• Randomly generated (generic) hyperplane:

  66*a + 45*b + 2*c + 41*d + 37*e + 46*f + 25*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 0 : -45/29 : 45/29 : 0 : -45/29]

  [1 : -22/15 : 0 : 0 : 0 : 0 : 0]

  [1 : -66/31 : 66/31 : 0 : 66/31 : 0 : -66/31]

  [0 : 1 : -1 : 0 : -68/37 : 0 : 1]

  [0 : 1 : -13/81 : 0 : -68/81 : -68/81 : 1]

  [0 : 1 : 0 : 13/87 : -1 : -74/87 : 1]

  [0 : 0 : 0 : 1 : -3/2 : -1/2 : 3/2]

  [0 : 0 : 0 : 0 : 1 : -6/23 : -1]

  [1 : -1 : 0 : 0 : -7/4 : 0 : 7/4]

  [1 : -1 : -33/2 : 0 : 1 : 0 : -1]

  [0 : 0 : 1 : 0 : -2/83 : -2/83 : 0]

  [0 : 0 : 0 : 0 : 1 : -37/46 : 0]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 666 bases, 258 non-bases

  • circuits:

    • 1 circuit of size 3:

      {0, 5, 6}

    • 2 circuits of size 4:

      {1, 2, 8, 9}, {3, 4, 10, 11}

    • 8 circuits of size 5:

      {0, 1, 5, 7, 8}, {0, 1, 6, 7, 8}, {1, 5, 6, 7, 8}, {2, 3, 4, 9, 10}, {2, 3, 4, 9, 11}, {2, 3, 9, 10, 11}, {2, 4, 9, 10, 11}, {7, 8, 9, 10, 11}

    • 69 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 4, 7, 9}, {0, 1, 2, 5, 7, 9}, {0, 1, 2, 6, 7, 9}, {1, 2, 5, 6, 7, 9}, {1, 3, 4, 7, 8, 9}, {2, 3, 4, 7, 8, 9}, {0, 2, 5, 7, 8, 9}, {0, 2, 6, 7, 8, 9}, {2, 5, 6, 7, 8, 9}, {1, 2, 3, 4, 7, 10}, {0, 3, 4, 5, 7, 10}, {0, 3, 4, 6, 7, 10}, {3, 4, 5, 6, 7, 10}, {1, 2, 3, 4, 8, 10}, {1, 2, 3, 7, 8, 10}, {1, 2, 4, 7, 8, 10}, {1, 3, 4, 7, 8, 10}, {2, 3, 4, 7, 8, 10}, {1, 2, 3, 7, 9, 10}, {1, 2, 4, 7, 9, 10}, {1, 3, 4, 7, 9, 10}, {1, 3, 4, 8, 9, 10}, {1, 3, 7, 8, 9, 10}, {2, 3, 7, 8, 9, 10}, {1, 4, 7, 8, 9, 10}, {2, 4, 7, 8, 9, 10}, {3, 4, 7, 8, 9, 10}, {1, 2, 3, 4, 7, 11}, {0, 3, 4, 5, 7, 11}, {0, 3, 4, 6, 7, 11}, {3, 4, 5, 6, 7, 11}, {1, 2, 3, 4, 8, 11}, {1, 2, 3, 7, 8, 11}, {1, 2, 4, 7, 8, 11}, {1, 3, 4, 7, 8, 11}, {2, 3, 4, 7, 8, 11}, {1, 2, 3, 7, 9, 11}, {1, 2, 4, 7, 9, 11}, {1, 3, 4, 7, 9, 11}, {1, 3, 4, 8, 9, 11}, {1, 3, 7, 8, 9, 11}, {2, 3, 7, 8, 9, 11}, {1, 4, 7, 8, 9, 11}, {2, 4, 7, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {1, 2, 3, 7, 10, 11}, {1, 2, 4, 7, 10, 11}, {0, 3, 5, 7, 10, 11}, {0, 4, 5, 7, 10, 11}, {0, 3, 6, 7, 10, 11}, {0, 4, 6, 7, 10, 11}, {3, 5, 6, 7, 10, 11}, {4, 5, 6, 7, 10, 11}, {1, 2, 3, 8, 10, 11}, {1, 2, 4, 8, 10, 11}, {1, 2, 7, 8, 10, 11}, {1, 3, 7, 8, 10, 11}, {2, 3, 7, 8, 10, 11}, {1, 4, 7, 8, 10, 11}, {2, 4, 7, 8, 10, 11}, {1, 2, 7, 9, 10, 11}, {1, 3, 7, 9, 10, 11}, {1, 4, 7, 9, 10, 11}, {1, 3, 8, 9, 10, 11}, {1, 4, 8, 9, 10, 11}

    • 204 circuits of size 7:

      {0, 2, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 5, 7, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 2, 3, 6, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 3, 6, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 1, 2, 3, 6, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {3, 4, 5, 6, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {4, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 5, 7, 11}, {0, 1, 2, 4, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {0, 1, 2, 4, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {3, 4, 5, 6, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {0, 4, 5, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {4, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {1, 4, 5, 6, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {0, 3, 5, 8, 9, 10, 11}, {0, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {3, 5, 6, 8, 9, 10, 11}, {4, 5, 6, 8, 9, 10, 11}

---

---

20. Graph1220:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {7,8}, {8,9}, {9,10}, {10,11}, {11,7}, {0,6}, {6,5}, {6,7}, {1,8}, {2,10}, {3,9}, {4,11}

• Randomly generated (generic) hyperplane:

  17*a + 71*b + 61*c + 63*d + 79*e + 64*f + 97*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : 0 : 5/11 : 0 : -6/11]

  [1 : 0 : -20/9 : 0 : 0 : 0 : 11/9]

  [1 : 44/71 : -1 : 0 : 0 : 0 : 0]

  [1 : -15/71 : 1 : -1 : 0 : 0 : 0]

  [1 : 47/133 : 47/133 : -47/133 : 0 : -86/133 : 0]

  [1 : 0 : 0 : 0 : 47/143 : -96/143 : 0]

  [0 : 0 : 0 : 0 : 1 : 16/3 : -13/3]

  [0 : 0 : 0 : 0 : 0 : 1 : -64/97]

  [0 : 0 : 1 : 0 : 0 : 0 : -61/97]

  [1 : 0 : 46/61 : -1 : 0 : 0 : 0]

  [1 : 2/3 : 2/3 : -5/3 : 0 : 0 : 0]

  [0 : 1 : 1 : -1 : 0 : -69/64 : 0]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 666 bases, 258 non-bases

  • circuits:

    • 1 circuit of size 3:

      {0, 5, 6}

    • 1 circuit of size 4:

      {2, 3, 9, 10}

    • 16 circuits of size 5:

      {0, 1, 5, 7, 8}, {0, 1, 6, 7, 8}, {1, 5, 6, 7, 8}, {1, 2, 3, 8, 9}, {1, 2, 3, 8, 10}, {1, 2, 8, 9, 10}, {1, 3, 8, 9, 10}, {0, 4, 5, 7, 11}, {0, 4, 6, 7, 11}, {4, 5, 6, 7, 11}, {1, 4, 7, 8, 11}, {2, 3, 4, 9, 11}, {2, 3, 4, 10, 11}, {2, 4, 9, 10, 11}, {3, 4, 9, 10, 11}, {7, 8, 9, 10, 11}

    • 48 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {1, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 7, 8}, {1, 2, 3, 4, 7, 9}, {1, 2, 4, 7, 8, 9}, {1, 3, 4, 7, 8, 9}, {2, 3, 4, 7, 8, 9}, {1, 2, 3, 4, 7, 10}, {1, 2, 4, 7, 8, 10}, {1, 3, 4, 7, 8, 10}, {2, 3, 4, 7, 8, 10}, {1, 2, 4, 7, 9, 10}, {1, 3, 4, 7, 9, 10}, {1, 4, 7, 8, 9, 10}, {2, 4, 7, 8, 9, 10}, {3, 4, 7, 8, 9, 10}, {1, 2, 3, 4, 7, 11}, {1, 2, 3, 4, 8, 11}, {0, 1, 4, 5, 8, 11}, {0, 1, 4, 6, 8, 11}, {1, 4, 5, 6, 8, 11}, {1, 2, 3, 7, 8, 11}, {2, 3, 4, 7, 8, 11}, {1, 2, 3, 7, 9, 11}, {1, 2, 4, 7, 9, 11}, {1, 3, 4, 7, 9, 11}, {1, 2, 4, 8, 9, 11}, {1, 3, 4, 8, 9, 11}, {1, 2, 7, 8, 9, 11}, {1, 3, 7, 8, 9, 11}, {2, 3, 7, 8, 9, 11}, {2, 4, 7, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {1, 2, 3, 7, 10, 11}, {1, 2, 4, 7, 10, 11}, {1, 3, 4, 7, 10, 11}, {1, 2, 4, 8, 10, 11}, {1, 3, 4, 8, 10, 11}, {1, 2, 7, 8, 10, 11}, {1, 3, 7, 8, 10, 11}, {2, 3, 7, 8, 10, 11}, {2, 4, 7, 8, 10, 11}, {3, 4, 7, 8, 10, 11}, {1, 2, 7, 9, 10, 11}, {1, 3, 7, 9, 10, 11}, {1, 4, 7, 9, 10, 11}, {1, 4, 8, 9, 10, 11}

    • 222 circuits of size 7:

      {0, 2, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 5, 7, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 3, 6, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 5, 7, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 3, 6, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {2, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {0, 1, 2, 6, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {3, 4, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {3, 4, 5, 6, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {4, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {3, 4, 5, 6, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {0, 2, 6, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 3, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {0, 3, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {3, 4, 5, 6, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {3, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {1, 4, 5, 6, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {3, 5, 6, 7, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {0, 3, 5, 8, 9, 10, 11}, {0, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {3, 5, 6, 8, 9, 10, 11}, {4, 5, 6, 8, 9, 10, 11}

---

---

21. Graph1221:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {5,6}, {6,7}, {7,8}, {8,9}, {9,5}, {0,5}, {4,9}, {6,10}, {1,10}, {2,10}, {7,11}, {11,8}, {3,11}

• Randomly generated (generic) hyperplane:

  88*a + 57*b + 76*c + 69*d + 76*e + 17*f + 53*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 0 : -8/29 : -8/29 : -1 : 0]

  [1 : -21/8 : 0 : 0 : 0 : 29/8 : 0]

  [1 : 0 : -105/59 : 0 : 0 : 164/59 : 0]

  [0 : 0 : 1 : 0 : 0 : -76/17 : 0]

  [0 : 0 : 0 : 1 : 1 : -145/17 : 0]

  [0 : 1 : 0 : 1 : -126/59 : 126/59 : 0]

  [0 : 1 : -126/145 : 19/145 : 0 : 0 : 0]

  [0 : 0 : 1 : -129/16 : 0 : 0 : 145/16]

  [0 : 0 : 0 : 1 : 0 : 0 : -69/53]

  [0 : 0 : 0 : 1 : -69/59 : 69/59 : 0]

  [1 : 164/19 : -145/19 : 0 : 0 : 0 : 0]

  [0 : 0 : 1 : 0 : 0 : 0 : -76/53]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 576 bases, 348 non-bases

  • circuits:

    • 2 circuits of size 3:

      {1, 2, 10}, {7, 8, 11}

    • 1 circuit of size 4:

      {0, 4, 5, 9}

    • 16 circuits of size 5:

      {0, 1, 2, 3, 4}, {0, 1, 2, 5, 6}, {0, 3, 4, 5, 6}, {0, 3, 4, 6, 9}, {0, 3, 5, 6, 9}, {3, 4, 5, 6, 9}, {3, 4, 7, 8, 9}, {5, 6, 7, 8, 9}, {0, 1, 3, 4, 10}, {0, 2, 3, 4, 10}, {0, 1, 5, 6, 10}, {0, 2, 5, 6, 10}, {3, 4, 7, 9, 11}, {5, 6, 7, 9, 11}, {3, 4, 8, 9, 11}, {5, 6, 8, 9, 11}

    • 57 circuits of size 6:

      {1, 2, 3, 4, 5, 6}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 5, 9}, {1, 2, 3, 4, 5, 9}, {0, 1, 2, 3, 6, 9}, {0, 1, 2, 4, 6, 9}, {1, 2, 3, 4, 6, 9}, {1, 2, 3, 5, 6, 9}, {1, 2, 4, 5, 6, 9}, {0, 3, 5, 7, 8, 9}, {0, 3, 6, 7, 8, 9}, {0, 4, 6, 7, 8, 9}, {1, 3, 4, 5, 6, 10}, {2, 3, 4, 5, 6, 10}, {1, 3, 6, 7, 8, 10}, {2, 3, 6, 7, 8, 10}, {0, 1, 3, 5, 9, 10}, {0, 2, 3, 5, 9, 10}, {1, 3, 4, 5, 9, 10}, {2, 3, 4, 5, 9, 10}, {0, 1, 3, 6, 9, 10}, {0, 2, 3, 6, 9, 10}, {0, 1, 4, 6, 9, 10}, {0, 2, 4, 6, 9, 10}, {1, 3, 4, 6, 9, 10}, {2, 3, 4, 6, 9, 10}, {1, 3, 5, 6, 9, 10}, {2, 3, 5, 6, 9, 10}, {1, 4, 5, 6, 9, 10}, {2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 7, 11}, {1, 2, 3, 6, 7, 11}, {0, 3, 4, 6, 7, 11}, {0, 3, 5, 6, 7, 11}, {0, 4, 5, 6, 7, 11}, {3, 4, 5, 6, 7, 11}, {0, 3, 4, 5, 8, 11}, {1, 2, 3, 6, 8, 11}, {0, 3, 4, 6, 8, 11}, {0, 3, 5, 6, 8, 11}, {0, 4, 5, 6, 8, 11}, {3, 4, 5, 6, 8, 11}, {0, 3, 5, 7, 9, 11}, {0, 3, 6, 7, 9, 11}, {0, 4, 6, 7, 9, 11}, {0, 3, 5, 8, 9, 11}, {0, 3, 6, 8, 9, 11}, {0, 4, 6, 8, 9, 11}, {1, 3, 6, 7, 10, 11}, {2, 3, 6, 7, 10, 11}, {1, 3, 6, 8, 10, 11}, {2, 3, 6, 8, 10, 11}

    • 108 circuits of size 7:

      {0, 1, 2, 3, 5, 7, 8}, {0, 1, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 2, 4, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 7, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 2, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 1, 2, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {0, 1, 6, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 5, 7, 11}, {0, 1, 2, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 2, 4, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 1, 2, 3, 7, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 2, 3, 8, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {2, 3, 4, 5, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {2, 3, 4, 5, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 2, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {2, 4, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {0, 1, 3, 8, 9, 10, 11}, {0, 2, 3, 8, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {2, 3, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {2, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}

---

---

22. Graph1222:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {0,6}, {6,8}, {8,5}, {6,7}, {7,8}, {7,9}, {9,10}, {3,10}, {9,11}, {4,11}, {2,11}, {1,10}

• Randomly generated (generic) hyperplane:

  61*a + 46*b + 64*c + 59*d + 76*e + 51*f + 96*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 0 : -23/4 : 0 : 23/4 : 0]

  [1 : -43/23 : 0 : 0 : 1 : -1 : 0]

  [1 : -1 : 0 : -8/31 : 1 : -1 : -8/31]

  [1 : 0 : 0 : -157/155 : 0 : 0 : -2/155]

  [1 : -157/58 : 0 : 157/58 : 157/58 : -157/58 : -99/58]

  [0 : 1 : 0 : -1 : 19/10 : 1 : -19/10]

  [0 : 0 : 1 : -21/2 : -1 : 21/2 : 1]

  [0 : 0 : 1 : 16/3 : 16/3 : -16/3 : -16/3]

  [0 : 0 : 1 : 0 : 16/5 : 0 : -16/5]

  [0 : 0 : 0 : 1 : 1 : -1 : -7/8]

  [1 : 0 : 0 : -43/42 : -1/42 : 1/42 : 0]

  [1 : -1 : 0 : 1 : 1 : -1 : -33/32]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 594 bases, 330 non-bases

  • circuits:

    • 1 circuit of size 3:

      {6, 7, 8}

    • 5 circuits of size 4:

      {0, 5, 6, 7}, {0, 5, 6, 8}, {0, 5, 7, 8}, {1, 2, 3, 10}, {2, 3, 4, 11}

    • 17 circuits of size 5:

      {1, 2, 3, 4, 9}, {1, 2, 4, 9, 10}, {1, 3, 4, 9, 10}, {2, 3, 4, 9, 10}, {0, 1, 5, 9, 10}, {1, 2, 3, 9, 11}, {1, 2, 4, 9, 11}, {1, 3, 4, 9, 11}, {0, 4, 5, 9, 11}, {1, 2, 4, 10, 11}, {1, 3, 4, 10, 11}, {1, 2, 9, 10, 11}, {1, 3, 9, 10, 11}, {2, 3, 9, 10, 11}, {1, 4, 9, 10, 11}, {2, 4, 9, 10, 11}, {3, 4, 9, 10, 11}

    • 37 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 5, 9}, {0, 1, 2, 4, 5, 9}, {0, 1, 3, 4, 5, 9}, {0, 2, 3, 4, 5, 9}, {0, 1, 2, 4, 5, 10}, {0, 1, 3, 4, 5, 10}, {0, 2, 3, 4, 5, 10}, {0, 2, 3, 5, 9, 10}, {0, 2, 4, 5, 9, 10}, {0, 3, 4, 5, 9, 10}, {0, 1, 6, 7, 9, 10}, {1, 5, 6, 7, 9, 10}, {0, 1, 6, 8, 9, 10}, {1, 5, 6, 8, 9, 10}, {0, 1, 7, 8, 9, 10}, {1, 5, 7, 8, 9, 10}, {0, 1, 2, 3, 5, 11}, {0, 1, 2, 4, 5, 11}, {0, 1, 3, 4, 5, 11}, {0, 1, 2, 5, 9, 11}, {0, 1, 3, 5, 9, 11}, {0, 2, 3, 5, 9, 11}, {0, 4, 6, 7, 9, 11}, {4, 5, 6, 7, 9, 11}, {0, 4, 6, 8, 9, 11}, {4, 5, 6, 8, 9, 11}, {0, 4, 7, 8, 9, 11}, {4, 5, 7, 8, 9, 11}, {0, 1, 2, 5, 10, 11}, {0, 1, 3, 5, 10, 11}, {0, 2, 3, 5, 10, 11}, {0, 1, 4, 5, 10, 11}, {0, 2, 4, 5, 10, 11}, {0, 3, 4, 5, 10, 11}, {0, 2, 5, 9, 10, 11}, {0, 3, 5, 9, 10, 11}

    • 150 circuits of size 7:

      {0, 1, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 1, 2, 3, 4, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 2, 3, 6, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 3, 6, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 2, 3, 7, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {2, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 2, 3, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {3, 4, 5, 6, 7, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {3, 4, 5, 6, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {0, 1, 2, 3, 6, 7, 11}, {0, 1, 2, 4, 6, 7, 11}, {0, 1, 3, 4, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {1, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 3, 7, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {0, 1, 2, 7, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 3, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {0, 1, 2, 6, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {3, 4, 5, 6, 7, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {3, 4, 5, 6, 8, 10, 11}, {0, 1, 2, 7, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {3, 4, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {3, 5, 6, 7, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {3, 5, 6, 8, 9, 10, 11}, {0, 2, 7, 8, 9, 10, 11}, {0, 3, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}, {3, 5, 7, 8, 9, 10, 11}

---

---

23. Graph1223:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {0,6}, {6,1}, {6,7}, {7,10}, {7,11}, {2,11}, {8,11}, {8,10}, {3,10}, {8,9}, {4,9}, {9,5}

• Randomly generated (generic) hyperplane:

  9*a + 36*b + 13*c + 3*d + 55*e + 40*f + 97*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : -9/13 : 0 : 0 : 0 : 0]

  [1 : 11/2 : 1 : 0 : 0 : -11/2 : 0]

  [0 : 1 : 0 : 0 : 4/55 : -1 : 0]

  [0 : 0 : 1 : 1 : -56/55 : 1 : 0]

  [0 : 0 : 1 : 28/65 : 28/65 : 28/65 : -37/65]

  [0 : 0 : 1 : 0 : 0 : 0 : -13/97]

  [1 : 9/17 : -9/17 : 0 : 0 : -9/17 : 0]

  [0 : 1 : -1 : 0 : 0 : -23/40 : 0]

  [0 : 0 : 1 : 41/49 : -8/49 : -8/49 : 0]

  [0 : 0 : 0 : 1 : 1 : 1 : -98/97]

  [0 : 0 : 1 : 1 : 0 : -2/5 : 0]

  [0 : 1 : -59/82 : 0 : -23/82 : -23/82 : 0]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 594 bases, 330 non-bases

  • circuits:

    • 2 circuits of size 3:

      {0, 1, 6}, {4, 5, 9}

    • 1 circuit of size 4:

      {7, 8, 10, 11}

    • 10 circuits of size 5:

      {3, 4, 5, 8, 10}, {2, 3, 7, 8, 10}, {3, 4, 8, 9, 10}, {3, 5, 8, 9, 10}, {0, 1, 2, 7, 11}, {0, 2, 6, 7, 11}, {1, 2, 6, 7, 11}, {2, 3, 7, 8, 11}, {2, 3, 7, 10, 11}, {2, 3, 8, 10, 11}

    • 75 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 7, 8}, {2, 3, 4, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {0, 1, 2, 3, 4, 9}, {0, 1, 2, 3, 5, 9}, {0, 2, 3, 4, 6, 9}, {1, 2, 3, 4, 6, 9}, {0, 2, 3, 5, 6, 9}, {1, 2, 3, 5, 6, 9}, {2, 3, 4, 7, 8, 9}, {2, 3, 5, 7, 8, 9}, {0, 1, 2, 3, 7, 10}, {2, 3, 4, 5, 7, 10}, {0, 2, 3, 6, 7, 10}, {1, 2, 3, 6, 7, 10}, {0, 1, 2, 3, 8, 10}, {0, 2, 3, 6, 8, 10}, {1, 2, 3, 6, 8, 10}, {0, 1, 2, 7, 8, 10}, {0, 1, 3, 7, 8, 10}, {2, 4, 5, 7, 8, 10}, {0, 2, 6, 7, 8, 10}, {1, 2, 6, 7, 8, 10}, {0, 3, 6, 7, 8, 10}, {1, 3, 6, 7, 8, 10}, {2, 3, 4, 7, 9, 10}, {2, 3, 5, 7, 9, 10}, {2, 4, 7, 8, 9, 10}, {2, 5, 7, 8, 9, 10}, {2, 3, 4, 5, 7, 11}, {0, 1, 2, 3, 8, 11}, {2, 3, 4, 5, 8, 11}, {0, 2, 3, 6, 8, 11}, {1, 2, 3, 6, 8, 11}, {0, 1, 3, 7, 8, 11}, {2, 4, 5, 7, 8, 11}, {3, 4, 5, 7, 8, 11}, {0, 3, 6, 7, 8, 11}, {1, 3, 6, 7, 8, 11}, {2, 3, 4, 7, 9, 11}, {2, 3, 5, 7, 9, 11}, {2, 3, 4, 8, 9, 11}, {2, 3, 5, 8, 9, 11}, {2, 4, 7, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {2, 5, 7, 8, 9, 11}, {3, 5, 7, 8, 9, 11}, {0, 1, 2, 3, 10, 11}, {2, 3, 4, 5, 10, 11}, {0, 2, 3, 6, 10, 11}, {1, 2, 3, 6, 10, 11}, {0, 1, 3, 7, 10, 11}, {2, 4, 5, 7, 10, 11}, {3, 4, 5, 7, 10, 11}, {0, 3, 6, 7, 10, 11}, {1, 3, 6, 7, 10, 11}, {0, 1, 2, 8, 10, 11}, {0, 1, 3, 8, 10, 11}, {2, 4, 5, 8, 10, 11}, {0, 2, 6, 8, 10, 11}, {1, 2, 6, 8, 10, 11}, {0, 3, 6, 8, 10, 11}, {1, 3, 6, 8, 10, 11}, {2, 3, 4, 9, 10, 11}, {2, 3, 5, 9, 10, 11}, {2, 4, 7, 9, 10, 11}, {3, 4, 7, 9, 10, 11}, {2, 5, 7, 9, 10, 11}, {3, 5, 7, 9, 10, 11}, {2, 4, 8, 9, 10, 11}, {2, 5, 8, 9, 10, 11}

    • 126 circuits of size 7:

      {0, 1, 2, 4, 5, 7, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 1, 2, 5, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {1, 2, 5, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 3, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 4, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {0, 5, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {0, 1, 3, 4, 5, 7, 11}, {0, 3, 4, 5, 6, 7, 11}, {1, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 4, 5, 6, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {0, 5, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 3, 4, 5, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {0, 3, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 4, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 4, 5, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 4, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {0, 5, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}

---

---

24. Graph1224:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,0}, {3,4}, {4,10}, {2,6}, {1,5}, {5,7}, {4,5}, {6,7}, {7,8}, {8,9}, {9,10}, {10,6}, {9,11}, {11,8}, {0,11}

• Randomly generated (generic) hyperplane:

  2*a + 66*b + 49*c + 32*d + 57*e + 93*f + 12*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 1 : 0 : 22/75 : -53/75 : 0]

  [0 : 0 : 1 : 106/61 : 1 : -106/61 : 0]

  [1 : 0 : -1 : -47/61 : 0 : 47/61 : 0]

  [1 : 0 : -91/44 : 0 : 0 : 47/44 : 0]

  [1 : 91/83 : 91/83 : -91/83 : 0 : -1 : 0]

  [0 : 1 : 84/167 : -84/167 : -83/167 : -83/167 : 0]

  [1 : -27/22 : 16/11 : -16/11 : 0 : 16/11 : 0]

  [0 : 1 : -21/10 : 21/10 : 11/10 : -1 : 0]

  [0 : 0 : 1 : -1 : -49/69 : 20/69 : -20/69]

  [0 : 0 : 1 : -1 : 0 : 1 : -55/6]

  [1 : -1 : 32/55 : -32/55 : 0 : 32/55 : 0]

  [0 : 0 : 0 : 0 : 1 : 1 : -25/2]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 684 bases, 240 non-bases

  • circuits:

    • 1 circuit of size 3:

      {8, 9, 11}

    • 1 circuit of size 4:

      {0, 1, 2, 3}

    • 10 circuits of size 5:

      {0, 1, 2, 4, 5}, {0, 1, 3, 4, 5}, {0, 2, 3, 4, 5}, {1, 2, 3, 4, 5}, {1, 2, 5, 6, 7}, {2, 3, 4, 6, 10}, {4, 5, 6, 7, 10}, {6, 7, 8, 9, 10}, {6, 7, 8, 10, 11}, {6, 7, 9, 10, 11}

    • 65 circuits of size 6:

      {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 6, 7}, {0, 1, 5, 7, 8, 9}, {4, 5, 6, 7, 8, 9}, {0, 1, 2, 4, 6, 10}, {0, 1, 3, 4, 6, 10}, {0, 1, 2, 5, 6, 10}, {0, 1, 3, 5, 6, 10}, {0, 2, 3, 5, 6, 10}, {1, 2, 3, 5, 6, 10}, {0, 1, 4, 5, 6, 10}, {0, 2, 4, 5, 6, 10}, {1, 2, 4, 5, 6, 10}, {0, 3, 4, 5, 6, 10}, {1, 3, 4, 5, 6, 10}, {0, 1, 2, 4, 7, 10}, {0, 1, 3, 4, 7, 10}, {0, 2, 3, 4, 7, 10}, {1, 2, 3, 4, 7, 10}, {0, 1, 2, 5, 7, 10}, {0, 1, 3, 5, 7, 10}, {0, 2, 3, 5, 7, 10}, {1, 2, 3, 5, 7, 10}, {0, 1, 4, 5, 7, 10}, {0, 2, 4, 5, 7, 10}, {1, 2, 4, 5, 7, 10}, {0, 3, 4, 5, 7, 10}, {1, 3, 4, 5, 7, 10}, {2, 3, 4, 5, 7, 10}, {0, 1, 2, 6, 7, 10}, {0, 1, 3, 6, 7, 10}, {0, 2, 3, 6, 7, 10}, {1, 2, 3, 6, 7, 10}, {0, 1, 4, 6, 7, 10}, {0, 2, 4, 6, 7, 10}, {1, 2, 4, 6, 7, 10}, {0, 3, 4, 6, 7, 10}, {1, 3, 4, 6, 7, 10}, {0, 1, 5, 6, 7, 10}, {0, 2, 5, 6, 7, 10}, {0, 3, 5, 6, 7, 10}, {1, 3, 5, 6, 7, 10}, {2, 3, 5, 6, 7, 10}, {0, 3, 4, 8, 9, 10}, {4, 5, 6, 8, 9, 10}, {4, 5, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 11}, {4, 5, 6, 7, 8, 11}, {0, 1, 5, 7, 9, 11}, {4, 5, 6, 7, 9, 11}, {0, 3, 4, 8, 10, 11}, {4, 5, 6, 8, 10, 11}, {4, 5, 7, 8, 10, 11}, {0, 3, 4, 9, 10, 11}, {4, 5, 6, 9, 10, 11}, {4, 5, 7, 9, 10, 11}

    • 234 circuits of size 7:

      {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 4, 6, 8, 9}, {0, 1, 2, 5, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {1, 2, 3, 4, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 1, 2, 6, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {1, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {0, 1, 2, 4, 8, 9, 10}, {1, 2, 3, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {2, 3, 4, 5, 8, 9, 10}, {0, 1, 2, 6, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {0, 1, 2, 7, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {1, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {2, 3, 4, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 1, 4, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 1, 2, 6, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {2, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {2, 3, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 1, 2, 7, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {1, 2, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {2, 3, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {1, 2, 3, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {1, 3, 4, 5, 9, 10, 11}, {2, 3, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 2, 3, 7, 9, 10, 11}, {1, 2, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {2, 3, 4, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}

---

---

25. Graph1225:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,0}, {1,9}, {9,2}, {7,8}, {8,9}, {3,10}, {4,8}, {0,7}, {7,10}, {10,11}, {6,11}, {11,5}

• Randomly generated (generic) hyperplane:

  21*a + 72*b + 95*c + 69*d + 22*e + 33*f + 99*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 1 : -95/102 : 0 : -95/102 : 0]

  [1 : 0 : 0 : 1/102 : -1 : 1/102 : 0]

  [1 : 0 : 0 : 0 : -21/22 : 0 : 0]

  [0 : 1 : -1 : 0 : -5/11 : 1 : 0]

  [0 : 1 : -38/41 : 3/41 : -1 : 1 : 0]

  [0 : 0 : 1 : 1 : 0 : 0 : -164/99]

  [0 : 0 : 1 : 1 : 0 : 263/66 : -197/66]

  [0 : 1 : -72/95 : 0 : 0 : 0 : 0]

  [0 : 1 : 0 : -9/10 : 9/10 : -9/10 : 0]

  [1 : 0 : 0 : -21/80 : 21/80 : -21/80 : 0]

  [0 : 1 : -1 : 0 : 0 : 23/33 : 0]

  [0 : 0 : 0 : 0 : 0 : 1 : -1/3]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 594 bases, 330 non-bases

  • circuits:

    • 2 circuits of size 3:

      {1, 2, 9}, {5, 6, 11}

    • 18 circuits of size 5:

      {1, 2, 3, 4, 8}, {0, 1, 2, 7, 8}, {0, 3, 4, 7, 8}, {1, 3, 4, 8, 9}, {2, 3, 4, 8, 9}, {0, 1, 7, 8, 9}, {0, 2, 7, 8, 9}, {3, 4, 5, 6, 10}, {0, 3, 4, 7, 10}, {0, 5, 6, 7, 10}, {0, 3, 4, 8, 10}, {0, 3, 7, 8, 10}, {0, 4, 7, 8, 10}, {3, 4, 7, 8, 10}, {3, 4, 5, 10, 11}, {3, 4, 6, 10, 11}, {0, 5, 7, 10, 11}, {0, 6, 7, 10, 11}

    • 54 circuits of size 6:

      {0, 1, 2, 3, 4, 7}, {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 8}, {0, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}, {0, 1, 3, 4, 7, 9}, {0, 2, 3, 4, 7, 9}, {0, 1, 2, 3, 4, 10}, {0, 1, 2, 3, 7, 10}, {0, 1, 2, 4, 7, 10}, {1, 2, 3, 4, 7, 10}, {0, 1, 2, 3, 8, 10}, {0, 1, 2, 4, 8, 10}, {0, 3, 5, 6, 8, 10}, {0, 4, 5, 6, 8, 10}, {1, 2, 3, 7, 8, 10}, {1, 2, 4, 7, 8, 10}, {3, 5, 6, 7, 8, 10}, {4, 5, 6, 7, 8, 10}, {0, 1, 3, 4, 9, 10}, {0, 2, 3, 4, 9, 10}, {0, 1, 3, 7, 9, 10}, {0, 2, 3, 7, 9, 10}, {0, 1, 4, 7, 9, 10}, {0, 2, 4, 7, 9, 10}, {1, 3, 4, 7, 9, 10}, {2, 3, 4, 7, 9, 10}, {0, 1, 3, 8, 9, 10}, {0, 2, 3, 8, 9, 10}, {0, 1, 4, 8, 9, 10}, {0, 2, 4, 8, 9, 10}, {1, 3, 7, 8, 9, 10}, {2, 3, 7, 8, 9, 10}, {1, 4, 7, 8, 9, 10}, {2, 4, 7, 8, 9, 10}, {0, 3, 4, 5, 7, 11}, {0, 3, 4, 6, 7, 11}, {0, 3, 4, 5, 8, 11}, {0, 3, 4, 6, 8, 11}, {0, 3, 5, 7, 8, 11}, {0, 4, 5, 7, 8, 11}, {3, 4, 5, 7, 8, 11}, {0, 3, 6, 7, 8, 11}, {0, 4, 6, 7, 8, 11}, {3, 4, 6, 7, 8, 11}, {0, 3, 5, 8, 10, 11}, {0, 4, 5, 8, 10, 11}, {0, 3, 6, 8, 10, 11}, {0, 4, 6, 8, 10, 11}, {3, 5, 7, 8, 10, 11}, {4, 5, 7, 8, 10, 11}, {3, 6, 7, 8, 10, 11}, {4, 6, 7, 8, 10, 11}

    • 144 circuits of size 7:

      {0, 1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 5, 6, 7}, {0, 1, 2, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 5, 6, 8}, {0, 1, 2, 4, 5, 6, 8}, {1, 2, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 1, 3, 4, 5, 6, 9}, {0, 2, 3, 4, 5, 6, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 5, 6, 10}, {0, 1, 2, 4, 5, 6, 10}, {1, 2, 3, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 1, 2, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 5, 11}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 7, 11}, {0, 1, 2, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {0, 1, 2, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 2, 3, 4, 5, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {2, 4, 5, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 3, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {2, 3, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {2, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {2, 3, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}, {1, 6, 7, 8, 9, 10, 11}, {2, 6, 7, 8, 9, 10, 11}

---

---

26. Graph1226:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {0,11}, {1,8}, {9,2}, {3,10}, {5,6}, {6,4}, {6,7}, {7,8}, {8,9}, {10,9}, {10,11}, {7,11}

• Randomly generated (generic) hyperplane:

  27*a + 24*b + 54*c + 2*d + 68*e + 50*f + 30*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : -1 : -25/118 : -25/118 : 0]

  [0 : 1 : 0 : 0 : -37/59 : 22/59 : 0]

  [0 : 1 : 0 : 0 : 0 : -27/10 : 37/10]

  [1 : -1/2 : 0 : 0 : 0 : 0 : -1/2]

  [1 : 0 : -27/32 : 27/32 : 0 : 27/32 : -27/32]

  [1 : 0 : -25/34 : -1 : 0 : 25/34 : -25/34]

  [0 : 0 : 1 : -17 : 0 : -1 : 1]

  [0 : 0 : 0 : 1 : -1/44 : -1/44 : 1/44]

  [0 : 1 : 0 : 0 : -1/2 : 1/2 : -1/2]

  [0 : 1 : 0 : 0 : 0 : -6/5 : 6/5]

  [1 : 1/8 : 0 : 0 : 0 : 0 : -1]

  [1 : 0 : 0 : 1/30 : 1/30 : 1/30 : -31/30]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 666 bases, 258 non-bases

  • circuits:

    • 1 circuit of size 3:

      {4, 5, 6}

    • 2 circuits of size 4:

      {1, 2, 8, 9}, {2, 3, 9, 10}

    • 8 circuits of size 5:

      {1, 2, 3, 8, 10}, {1, 3, 8, 9, 10}, {0, 4, 5, 7, 11}, {0, 4, 6, 7, 11}, {0, 5, 6, 7, 11}, {0, 1, 7, 8, 11}, {0, 3, 7, 10, 11}, {7, 8, 9, 10, 11}

    • 68 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 1, 2, 3, 7, 9}, {0, 1, 3, 7, 8, 9}, {0, 2, 3, 7, 8, 9}, {0, 1, 2, 3, 7, 10}, {0, 3, 4, 5, 7, 10}, {0, 3, 4, 6, 7, 10}, {0, 3, 5, 6, 7, 10}, {0, 1, 2, 7, 8, 10}, {0, 1, 3, 7, 8, 10}, {0, 2, 3, 7, 8, 10}, {0, 1, 2, 7, 9, 10}, {0, 1, 3, 7, 9, 10}, {0, 1, 7, 8, 9, 10}, {0, 2, 7, 8, 9, 10}, {0, 3, 7, 8, 9, 10}, {0, 1, 2, 3, 7, 11}, {0, 1, 2, 3, 8, 11}, {0, 1, 4, 5, 8, 11}, {0, 1, 4, 6, 8, 11}, {0, 1, 5, 6, 8, 11}, {0, 2, 3, 7, 8, 11}, {1, 2, 3, 7, 8, 11}, {1, 4, 5, 7, 8, 11}, {1, 4, 6, 7, 8, 11}, {1, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 9, 11}, {0, 1, 2, 7, 9, 11}, {0, 1, 3, 7, 9, 11}, {0, 2, 3, 7, 9, 11}, {1, 2, 3, 7, 9, 11}, {0, 1, 3, 8, 9, 11}, {0, 2, 3, 8, 9, 11}, {0, 2, 7, 8, 9, 11}, {0, 3, 7, 8, 9, 11}, {1, 3, 7, 8, 9, 11}, {2, 3, 7, 8, 9, 11}, {0, 1, 2, 3, 10, 11}, {0, 3, 4, 5, 10, 11}, {0, 3, 4, 6, 10, 11}, {0, 3, 5, 6, 10, 11}, {0, 1, 2, 7, 10, 11}, {1, 2, 3, 7, 10, 11}, {3, 4, 5, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {3, 5, 6, 7, 10, 11}, {0, 1, 2, 8, 10, 11}, {0, 1, 3, 8, 10, 11}, {0, 2, 3, 8, 10, 11}, {0, 2, 7, 8, 10, 11}, {1, 2, 7, 8, 10, 11}, {1, 3, 7, 8, 10, 11}, {2, 3, 7, 8, 10, 11}, {0, 1, 2, 9, 10, 11}, {0, 1, 3, 9, 10, 11}, {0, 1, 7, 9, 10, 11}, {0, 2, 7, 9, 10, 11}, {1, 2, 7, 9, 10, 11}, {1, 3, 7, 9, 10, 11}, {0, 1, 8, 9, 10, 11}, {0, 2, 8, 9, 10, 11}, {0, 3, 8, 9, 10, 11}

    • 207 circuits of size 7:

      {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 7, 8}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {0, 1, 2, 5, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {0, 1, 2, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 1, 2, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {0, 5, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {1, 2, 3, 4, 5, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 2, 3, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 2, 3, 4, 5, 9, 11}, {1, 2, 3, 4, 5, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {2, 3, 4, 5, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {3, 4, 5, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 4, 5, 10, 11}, {1, 2, 3, 4, 5, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {2, 3, 4, 5, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {1, 3, 4, 5, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {2, 4, 5, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {0, 4, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {2, 4, 5, 8, 9, 10, 11}, {3, 4, 5, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {3, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {3, 5, 6, 8, 9, 10, 11}

---

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27. Graph1227:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,0}, {1,4}, {2,5}, {4,5}, {5,6}, {6,7}, {7,4}, {7,8}, {8,9}, {9,10}, {10,6}, {10,11}, {11,9}, {3,8}, {0,11}

• Randomly generated (generic) hyperplane:

  86*a + 80*b + 9*c + 63*d + 10*e + 29*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : -61/72 : -61/72 : 1 : 1 : -1]

  [0 : 0 : 1 : -1/7 : 0 : 0 : 0]

  [1 : 0 : 0 : -86/63 : 0 : 0 : 0]

  [1 : -86/61 : 0 : 0 : -86/61 : -86/61 : 86/61]

  [1 : 0 : -11/3 : -1 : 1 : 1 : 0]

  [1 : 0 : 0 : -1 : -23/10 : -23/10 : 0]

  [0 : 0 : 0 : 0 : 1 : 39/29 : -10/29]

  [1 : 0 : -1 : -1 : 5/13 : 1 : -8/13]

  [1 : 5/54 : -49/54 : -49/54 : 5/54 : 1 : -1]

  [0 : 1 : 1 : 1 : 181/19 : 162/19 : -162/19]

  [0 : 1 : 1 : 1 : 0 : 152/29 : -152/29]

  [0 : 1 : 1 : 1 : 8 : 8 : -8]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 636 bases, 288 non-bases

  • circuits:

    • 1 circuit of size 3:

      {9, 10, 11}

    • 3 circuits of size 4:

      {0, 1, 2, 3}, {1, 2, 4, 5}, {4, 5, 6, 7}

    • 11 circuits of size 5:

      {0, 1, 3, 4, 5}, {0, 2, 3, 4, 5}, {1, 2, 4, 6, 7}, {1, 2, 5, 6, 7}, {0, 3, 6, 7, 8}, {0, 3, 8, 9, 10}, {6, 7, 8, 9, 10}, {0, 3, 8, 9, 11}, {6, 7, 8, 9, 11}, {0, 3, 8, 10, 11}, {6, 7, 8, 10, 11}

    • 55 circuits of size 6:

      {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 6, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 6, 8}, {0, 1, 4, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {0, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 6, 8}, {0, 1, 2, 4, 7, 8}, {0, 1, 3, 4, 7, 8}, {0, 2, 3, 4, 7, 8}, {1, 2, 3, 4, 7, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 5, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 7, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 7, 8}, {0, 1, 2, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {0, 3, 6, 7, 9, 10}, {0, 1, 2, 8, 9, 10}, {1, 2, 3, 8, 9, 10}, {4, 5, 6, 8, 9, 10}, {4, 5, 7, 8, 9, 10}, {0, 3, 6, 7, 9, 11}, {0, 1, 2, 8, 9, 11}, {1, 2, 3, 8, 9, 11}, {4, 5, 6, 8, 9, 11}, {4, 5, 7, 8, 9, 11}, {0, 3, 6, 7, 10, 11}, {0, 1, 2, 8, 10, 11}, {1, 2, 3, 8, 10, 11}, {4, 5, 6, 8, 10, 11}, {4, 5, 7, 8, 10, 11}

    • 180 circuits of size 7:

      {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {2, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {2, 3, 4, 5, 7, 9, 10}, {0, 1, 2, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {2, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {2, 3, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {2, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {2, 3, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {2, 3, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 4, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {0, 3, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {2, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {0, 3, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {2, 3, 4, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {2, 3, 4, 6, 7, 10, 11}, {0, 1, 5, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {2, 3, 4, 5, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {2, 3, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}

---

---

28. Graph1228:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,5}, {5,1}, {3,8}, {4,7}, {5,6}, {6,7}, {7,8}, {8,9}, {9,10}, {10,6}, {10,11}, {11,9}, {0,11}

• Randomly generated (generic) hyperplane:

  31*a + 7*b + 60*c + 20*d + 71*e + 18*f + 7*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : -31/109 : -31/109 : -31/109 : 0]

  [1 : 31/82 : 0 : 0 : -31/82 : -31/82 : 0]

  [1 : 26/9 : 0 : 17/9 : -1 : -1 : 0]

  [0 : 1 : 0 : -7/20 : 0 : 0 : 0]

  [0 : 1 : -7/85 : 0 : 0 : -7/85 : -7/85]

  [0 : 1 : -41/2 : 0 : 39/2 : -1 : -41/2]

  [0 : 0 : 1 : 0 : -1 : 4/25 : 29/25]

  [0 : 0 : 1 : 0 : 0 : -12/5 : -12/5]

  [0 : 0 : 1 : -3 : 0 : 0 : 0]

  [0 : 0 : 1 : 1 : -5/6 : -5/6 : -5/6]

  [0 : 0 : 1 : 29/13 : -1 : -1 : -29/13]

  [0 : 0 : 0 : 1 : -13/96 : -13/96 : -109/96]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 576 bases, 348 non-bases

  • circuits:

    • 2 circuits of size 3:

      {0, 1, 2}, {9, 10, 11}

    • 2 circuits of size 4:

      {4, 5, 6, 7}, {3, 4, 7, 8}

    • 8 circuits of size 5:

      {0, 1, 3, 4, 5}, {0, 2, 3, 4, 5}, {1, 2, 3, 4, 5}, {3, 4, 5, 6, 8}, {3, 5, 6, 7, 8}, {6, 7, 8, 9, 10}, {6, 7, 8, 9, 11}, {6, 7, 8, 10, 11}

    • 78 circuits of size 6:

      {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 6, 7}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 6, 8}, {0, 1, 4, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 6, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 5, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {0, 1, 4, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {0, 1, 5, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {0, 1, 5, 6, 9, 10}, {0, 2, 5, 6, 9, 10}, {1, 2, 5, 6, 9, 10}, {3, 4, 5, 6, 9, 10}, {3, 4, 5, 7, 9, 10}, {3, 4, 6, 7, 9, 10}, {3, 5, 6, 7, 9, 10}, {0, 1, 3, 8, 9, 10}, {0, 2, 3, 8, 9, 10}, {1, 2, 3, 8, 9, 10}, {3, 4, 5, 8, 9, 10}, {3, 4, 6, 8, 9, 10}, {3, 5, 6, 8, 9, 10}, {4, 5, 6, 8, 9, 10}, {3, 5, 7, 8, 9, 10}, {4, 5, 7, 8, 9, 10}, {0, 1, 5, 6, 9, 11}, {0, 2, 5, 6, 9, 11}, {1, 2, 5, 6, 9, 11}, {3, 4, 5, 6, 9, 11}, {3, 4, 5, 7, 9, 11}, {3, 4, 6, 7, 9, 11}, {3, 5, 6, 7, 9, 11}, {0, 1, 3, 8, 9, 11}, {0, 2, 3, 8, 9, 11}, {1, 2, 3, 8, 9, 11}, {3, 4, 5, 8, 9, 11}, {3, 4, 6, 8, 9, 11}, {3, 5, 6, 8, 9, 11}, {4, 5, 6, 8, 9, 11}, {3, 5, 7, 8, 9, 11}, {4, 5, 7, 8, 9, 11}, {0, 1, 5, 6, 10, 11}, {0, 2, 5, 6, 10, 11}, {1, 2, 5, 6, 10, 11}, {3, 4, 5, 6, 10, 11}, {3, 4, 5, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {3, 5, 6, 7, 10, 11}, {0, 1, 3, 8, 10, 11}, {0, 2, 3, 8, 10, 11}, {1, 2, 3, 8, 10, 11}, {3, 4, 5, 8, 10, 11}, {3, 4, 6, 8, 10, 11}, {3, 5, 6, 8, 10, 11}, {4, 5, 6, 8, 10, 11}, {3, 5, 7, 8, 10, 11}, {4, 5, 7, 8, 10, 11}

    • 90 circuits of size 7:

      {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}

---

---

29. Graph1229:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {1,4}, {3,5}, {4,5}, {3,6}, {4,7}, {6,7}, {7,8}, {8,9}, {9,6}, {9,10}, {10,8}, {0,11}, {5,11}, {10,11}

• Randomly generated (generic) hyperplane:

  69*a + 67*b + 79*c + 7*d + 35*e + 33*f + 25*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : -69/97 : 69/97 : 0 : 0 : -69/97]

  [1 : -69/85 : 0 : 69/85 : 0 : 0 : -69/85]

  [1 : -7/3 : 4/3 : 1 : 0 : 0 : -1]

  [0 : 1 : -1 : 12/7 : 0 : 0 : 0]

  [0 : 1 : 0 : 67/18 : 0 : 0 : -67/18]

  [0 : 1 : -67/72 : 67/72 : 0 : 0 : 0]

  [0 : 0 : 0 : 1 : -1/5 : 0 : 0]

  [0 : 0 : 0 : 1 : 3/10 : 0 : -7/10]

  [0 : 0 : 0 : 0 : 1 : -30/29 : -1/29]

  [0 : 0 : 0 : 0 : 1 : -35/58 : -35/58]

  [0 : 0 : 0 : 0 : 1 : -1 : -2/25]

  [0 : 0 : 1 : -1 : 0 : 0 : -72/25]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 540 bases, 384 non-bases

  • circuits:

    • 2 circuits of size 3:

      {0, 1, 2}, {8, 9, 10}

    • 4 circuits of size 4:

      {6, 7, 8, 9}, {6, 7, 8, 10}, {6, 7, 9, 10}, {3, 4, 5, 11}

    • 16 circuits of size 5:

      {0, 1, 3, 4, 5}, {0, 2, 3, 4, 5}, {1, 2, 3, 4, 5}, {3, 4, 5, 6, 7}, {0, 1, 3, 4, 11}, {0, 2, 3, 4, 11}, {1, 2, 3, 4, 11}, {0, 1, 3, 5, 11}, {0, 2, 3, 5, 11}, {1, 2, 3, 5, 11}, {0, 1, 4, 5, 11}, {0, 2, 4, 5, 11}, {1, 2, 4, 5, 11}, {3, 4, 6, 7, 11}, {3, 5, 6, 7, 11}, {4, 5, 6, 7, 11}

    • 42 circuits of size 6:

      {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 6, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {3, 4, 5, 6, 8, 9}, {3, 4, 5, 7, 8, 9}, {3, 4, 5, 6, 8, 10}, {3, 4, 5, 7, 8, 10}, {3, 4, 5, 6, 9, 10}, {3, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 11}, {0, 2, 3, 6, 7, 11}, {1, 2, 3, 6, 7, 11}, {0, 1, 4, 6, 7, 11}, {0, 2, 4, 6, 7, 11}, {1, 2, 4, 6, 7, 11}, {0, 1, 5, 6, 7, 11}, {0, 2, 5, 6, 7, 11}, {1, 2, 5, 6, 7, 11}, {3, 4, 6, 8, 9, 11}, {3, 5, 6, 8, 9, 11}, {4, 5, 6, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {3, 5, 7, 8, 9, 11}, {4, 5, 7, 8, 9, 11}, {3, 4, 6, 8, 10, 11}, {3, 5, 6, 8, 10, 11}, {4, 5, 6, 8, 10, 11}, {3, 4, 7, 8, 10, 11}, {3, 5, 7, 8, 10, 11}, {4, 5, 7, 8, 10, 11}, {3, 4, 6, 9, 10, 11}, {3, 5, 6, 9, 10, 11}, {4, 5, 6, 9, 10, 11}, {3, 4, 7, 9, 10, 11}, {3, 5, 7, 9, 10, 11}, {4, 5, 7, 9, 10, 11}

    • 108 circuits of size 7:

      {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 4, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {1, 2, 3, 4, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 3, 7, 8, 9, 11}, {1, 2, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {1, 2, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 2, 3, 7, 9, 10, 11}, {1, 2, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}

---

---

30. Graph1230:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,0}, {1,9}, {9,2}, {6,8}, {8,9}, {8,10}, {10,7}, {3,10}, {5,11}, {11,4}, {0,11}

• Randomly generated (generic) hyperplane:

  24*a + 79*b + 86*c + 6*d + 80*e + 53*f + 35*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 0 : -44/51 : -44/51 : 0 : -7/51]

  [1 : -9/22 : 0 : -1 : 0 : 0 : 9/22]

  [1 : 0 : 0 : -4 : 0 : 0 : 0]

  [0 : 0 : 1 : -131/6 : 1 : 0 : -1]

  [0 : 0 : 1 : 139/2 : 139/2 : -137/2 : 139/2]

  [0 : 0 : 1 : 0 : 0 : -86/53 : 0]

  [0 : 1 : 21/43 : -1 : -1 : 0 : -1]

  [0 : 1 : 0 : -1 : -1 : 0 : 1/5]

  [0 : 1 : -19/83 : -1 : -19/83 : 0 : -1]

  [1 : -12/19 : 0 : 12/19 : 0 : 0 : 12/19]

  [0 : 0 : 1 : 0 : 1 : 0 : -166/35]

  [0 : 0 : 0 : 1 : 1 : -51/53 : -1]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 594 bases, 330 non-bases

  • circuits:

    • 2 circuits of size 3:

      {1, 2, 9}, {4, 5, 11}

    • 1 circuit of size 4:

      {6, 7, 8, 10}

    • 10 circuits of size 5:

      {0, 4, 5, 6, 7}, {0, 3, 6, 7, 8}, {0, 3, 6, 7, 10}, {1, 2, 3, 8, 10}, {0, 3, 6, 8, 10}, {0, 3, 7, 8, 10}, {1, 3, 8, 9, 10}, {2, 3, 8, 9, 10}, {0, 4, 6, 7, 11}, {0, 5, 6, 7, 11}

    • 75 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 6, 7}, {0, 1, 2, 3, 6, 8}, {0, 3, 4, 5, 6, 8}, {0, 1, 2, 3, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 1, 2, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {3, 4, 5, 6, 7, 8}, {0, 1, 3, 4, 5, 9}, {0, 2, 3, 4, 5, 9}, {0, 1, 3, 6, 7, 9}, {0, 2, 3, 6, 7, 9}, {0, 1, 3, 6, 8, 9}, {0, 2, 3, 6, 8, 9}, {0, 1, 3, 7, 8, 9}, {0, 2, 3, 7, 8, 9}, {0, 1, 6, 7, 8, 9}, {0, 2, 6, 7, 8, 9}, {1, 3, 6, 7, 8, 9}, {2, 3, 6, 7, 8, 9}, {0, 1, 2, 3, 6, 10}, {0, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 7, 10}, {0, 3, 4, 5, 7, 10}, {0, 1, 2, 6, 7, 10}, {1, 2, 3, 6, 7, 10}, {3, 4, 5, 6, 7, 10}, {0, 3, 4, 5, 8, 10}, {0, 1, 2, 6, 8, 10}, {0, 4, 5, 6, 8, 10}, {3, 4, 5, 6, 8, 10}, {0, 1, 2, 7, 8, 10}, {0, 4, 5, 7, 8, 10}, {3, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 9, 10}, {0, 2, 3, 6, 9, 10}, {0, 1, 3, 7, 9, 10}, {0, 2, 3, 7, 9, 10}, {0, 1, 6, 7, 9, 10}, {0, 2, 6, 7, 9, 10}, {1, 3, 6, 7, 9, 10}, {2, 3, 6, 7, 9, 10}, {0, 1, 6, 8, 9, 10}, {0, 2, 6, 8, 9, 10}, {0, 1, 7, 8, 9, 10}, {0, 2, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 11}, {0, 1, 2, 3, 5, 11}, {0, 3, 4, 6, 8, 11}, {0, 3, 5, 6, 8, 11}, {0, 3, 4, 7, 8, 11}, {0, 3, 5, 7, 8, 11}, {3, 4, 6, 7, 8, 11}, {3, 5, 6, 7, 8, 11}, {0, 1, 3, 4, 9, 11}, {0, 2, 3, 4, 9, 11}, {0, 1, 3, 5, 9, 11}, {0, 2, 3, 5, 9, 11}, {0, 3, 4, 6, 10, 11}, {0, 3, 5, 6, 10, 11}, {0, 3, 4, 7, 10, 11}, {0, 3, 5, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {3, 5, 6, 7, 10, 11}, {0, 3, 4, 8, 10, 11}, {0, 3, 5, 8, 10, 11}, {0, 4, 6, 8, 10, 11}, {3, 4, 6, 8, 10, 11}, {0, 5, 6, 8, 10, 11}, {3, 5, 6, 8, 10, 11}, {0, 4, 7, 8, 10, 11}, {3, 4, 7, 8, 10, 11}, {0, 5, 7, 8, 10, 11}, {3, 5, 7, 8, 10, 11}

    • 126 circuits of size 7:

      {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 1, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 4, 5, 6, 10}, {1, 2, 3, 4, 5, 6, 10}, {0, 1, 2, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {2, 3, 4, 5, 6, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {2, 3, 4, 5, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {1, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 2, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 2, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {2, 3, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {2, 3, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {2, 3, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {2, 4, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}

---

---

31. Graph1231:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,0}, {1,9}, {9,2}, {9,8}, {0,7}, {7,8}, {7,3}, {8,10}, {10,5}, {10,11}, {6,11}, {11,4}

• Randomly generated (generic) hyperplane:

  5*a + 74*b + 94*c + 97*d + 10*e + 56*f + 95*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 0 : 0 : -37/5 : 0 : 0]

  [1 : -33/28 : 1 : 0 : -33/28 : 0 : 0]

  [1 : -33/56 : 23/56 : 0 : 0 : 0 : 0]

  [0 : 1 : 1 : -56/51 : 0 : -56/51 : 0]

  [0 : 0 : 0 : 1 : 0 : -2/151 : -153/151]

  [0 : 0 : 0 : 1 : 0 : 0 : -97/95]

  [0 : 0 : 0 : 1 : -97/10 : 0 : 0]

  [0 : 1 : 74/59 : -74/59 : 0 : -74/59 : 0]

  [0 : 0 : 1 : -84/143 : -59/143 : -84/143 : 0]

  [1 : -1 : 23/28 : 0 : -23/28 : 0 : 0]

  [0 : 0 : 0 : 1 : -1 : 1 : -143/95]

  [0 : 0 : 0 : 1 : -1 : -87/151 : -87/151]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 600 bases, 324 non-bases

  • circuits:

    • 1 circuit of size 3:

      {1, 2, 9}

    • 6 circuits of size 4:

      {0, 3, 7, 8}, {4, 5, 6, 10}, {4, 5, 6, 11}, {4, 5, 10, 11}, {4, 6, 10, 11}, {5, 6, 10, 11}

    • 12 circuits of size 5:

      {0, 1, 2, 3, 7}, {0, 1, 2, 3, 8}, {0, 1, 2, 7, 8}, {1, 2, 3, 7, 8}, {0, 1, 3, 7, 9}, {0, 2, 3, 7, 9}, {0, 1, 3, 8, 9}, {0, 2, 3, 8, 9}, {0, 1, 7, 8, 9}, {0, 2, 7, 8, 9}, {1, 3, 7, 8, 9}, {2, 3, 7, 8, 9}

    • 40 circuits of size 6:

      {0, 3, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 8}, {0, 4, 5, 6, 7, 8}, {3, 4, 5, 6, 7, 8}, {0, 3, 4, 5, 7, 10}, {0, 3, 4, 6, 7, 10}, {0, 3, 5, 6, 7, 10}, {0, 3, 4, 5, 8, 10}, {0, 3, 4, 6, 8, 10}, {0, 3, 5, 6, 8, 10}, {0, 4, 5, 7, 8, 10}, {3, 4, 5, 7, 8, 10}, {0, 4, 6, 7, 8, 10}, {3, 4, 6, 7, 8, 10}, {0, 5, 6, 7, 8, 10}, {3, 5, 6, 7, 8, 10}, {0, 3, 4, 5, 7, 11}, {0, 3, 4, 6, 7, 11}, {0, 3, 5, 6, 7, 11}, {0, 3, 4, 5, 8, 11}, {0, 3, 4, 6, 8, 11}, {0, 3, 5, 6, 8, 11}, {0, 4, 5, 7, 8, 11}, {3, 4, 5, 7, 8, 11}, {0, 4, 6, 7, 8, 11}, {3, 4, 6, 7, 8, 11}, {0, 5, 6, 7, 8, 11}, {3, 5, 6, 7, 8, 11}, {0, 3, 4, 7, 10, 11}, {0, 3, 5, 7, 10, 11}, {0, 3, 6, 7, 10, 11}, {0, 3, 4, 8, 10, 11}, {0, 3, 5, 8, 10, 11}, {0, 3, 6, 8, 10, 11}, {0, 4, 7, 8, 10, 11}, {3, 4, 7, 8, 10, 11}, {0, 5, 7, 8, 10, 11}, {3, 5, 7, 8, 10, 11}, {0, 6, 7, 8, 10, 11}, {3, 6, 7, 8, 10, 11}

    • 180 circuits of size 7:

      {0, 1, 2, 3, 4, 5, 6}, {0, 1, 2, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 1, 3, 4, 5, 6, 9}, {0, 2, 3, 4, 5, 6, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 5, 10}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 1, 2, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 1, 2, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 2, 3, 4, 5, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {2, 3, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {2, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 5, 11}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 1, 2, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 2, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 1, 2, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 2, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 2, 3, 4, 5, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {2, 3, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 4, 10, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 2, 3, 4, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {2, 3, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 3, 6, 7, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {1, 3, 4, 8, 9, 10, 11}, {2, 3, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {2, 3, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {2, 3, 6, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {2, 4, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}, {1, 6, 7, 8, 9, 10, 11}, {2, 6, 7, 8, 9, 10, 11}

---

---

32. Graph1232:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {5,6}, {6,4}, {7,3}, {7,8}, {8,9}, {9,2}, {0,8}, {9,10}, {10,1}, {10,11}, {6,11}, {11,7}

• Randomly generated (generic) hyperplane:

  29*a + 84*b + 85*c + 27*d + 2*e + 6*f + 59*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : -123/25 : 0 : 1 : 1 : 1 : 148/25]

  [0 : 1 : -25/26 : 0 : 0 : 0 : -1/26]

  [0 : 1 : -1 : 0 : 0 : 0 : 1/59]

  [1 : 0 : 0 : 0 : 0 : 0 : -29/59]

  [1 : -29/184 : 0 : -29/184 : -29/184 : -29/92 : -29/184]

  [1 : 123/4 : 0 : -119/4 : -119/4 : 1 : -119/4]

  [1 : 1 : 0 : -119/94 : -119/94 : -25/94 : -119/94]

  [1 : 0 : 0 : 0 : 30/67 : 30/67 : -37/67]

  [1 : -1/3 : 0 : -1/3 : 1 : 1 : 0]

  [0 : 1 : -111/53 : -58/53 : 0 : 0 : 111/53]

  [0 : 0 : 1 : -26/27 : 0 : 0 : -1]

  [0 : 0 : 0 : 1 : -27/67 : -27/67 : -27/67]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 684 bases, 240 non-bases

  • circuits:

    • 1 circuit of size 3:

      {4, 5, 6}

    • 1 circuit of size 4:

      {1, 2, 9, 10}

    • 10 circuits of size 5:

      {0, 1, 2, 8, 9}, {2, 3, 7, 8, 9}, {0, 1, 2, 8, 10}, {0, 1, 8, 9, 10}, {0, 2, 8, 9, 10}, {3, 4, 5, 7, 11}, {3, 4, 6, 7, 11}, {3, 5, 6, 7, 11}, {0, 3, 7, 8, 11}, {7, 8, 9, 10, 11}

    • 65 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 3, 7, 8}, {0, 3, 4, 5, 7, 8}, {0, 3, 4, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {0, 1, 2, 3, 7, 9}, {0, 1, 3, 7, 8, 9}, {0, 1, 2, 3, 7, 10}, {0, 1, 3, 7, 8, 10}, {0, 2, 3, 7, 8, 10}, {1, 2, 3, 7, 8, 10}, {0, 1, 3, 7, 9, 10}, {0, 2, 3, 7, 9, 10}, {0, 3, 7, 8, 9, 10}, {1, 3, 7, 8, 9, 10}, {0, 1, 2, 3, 7, 11}, {0, 1, 2, 3, 8, 11}, {0, 3, 4, 5, 8, 11}, {0, 3, 4, 6, 8, 11}, {0, 3, 5, 6, 8, 11}, {0, 1, 2, 7, 8, 11}, {1, 2, 3, 7, 8, 11}, {0, 4, 5, 7, 8, 11}, {0, 4, 6, 7, 8, 11}, {0, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 9, 11}, {0, 1, 2, 7, 9, 11}, {0, 1, 3, 7, 9, 11}, {0, 2, 3, 7, 9, 11}, {1, 2, 3, 7, 9, 11}, {0, 1, 3, 8, 9, 11}, {0, 2, 3, 8, 9, 11}, {1, 2, 3, 8, 9, 11}, {0, 1, 7, 8, 9, 11}, {0, 2, 7, 8, 9, 11}, {1, 2, 7, 8, 9, 11}, {1, 3, 7, 8, 9, 11}, {0, 1, 2, 3, 10, 11}, {0, 1, 4, 5, 10, 11}, {0, 1, 4, 6, 10, 11}, {0, 1, 5, 6, 10, 11}, {0, 1, 2, 7, 10, 11}, {0, 1, 3, 7, 10, 11}, {0, 2, 3, 7, 10, 11}, {1, 2, 3, 7, 10, 11}, {0, 1, 3, 8, 10, 11}, {0, 2, 3, 8, 10, 11}, {1, 2, 3, 8, 10, 11}, {0, 1, 7, 8, 10, 11}, {0, 2, 7, 8, 10, 11}, {1, 2, 7, 8, 10, 11}, {1, 3, 7, 8, 10, 11}, {2, 3, 7, 8, 10, 11}, {0, 1, 3, 9, 10, 11}, {0, 2, 3, 9, 10, 11}, {0, 1, 7, 9, 10, 11}, {0, 2, 7, 9, 10, 11}, {0, 3, 7, 9, 10, 11}, {1, 3, 7, 9, 10, 11}, {2, 3, 7, 9, 10, 11}, {0, 3, 8, 9, 10, 11}, {1, 3, 8, 9, 10, 11}, {2, 3, 8, 9, 10, 11}

    • 234 circuits of size 7:

      {0, 1, 2, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 2, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 7, 8}, {0, 1, 2, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 7, 8}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {0, 1, 2, 5, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {1, 2, 3, 4, 5, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 4, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {0, 1, 5, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {1, 2, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 1, 2, 5, 6, 7, 10}, {0, 1, 3, 5, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 1, 5, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 2, 3, 4, 5, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {2, 3, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {2, 3, 4, 5, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {0, 5, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 4, 5, 7, 11}, {0, 1, 2, 4, 6, 7, 11}, {0, 1, 2, 5, 6, 7, 11}, {0, 1, 2, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 2, 3, 4, 5, 9, 11}, {1, 2, 3, 4, 5, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {2, 3, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {0, 2, 3, 4, 5, 10, 11}, {1, 2, 3, 4, 5, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {2, 3, 4, 5, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {1, 5, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {0, 3, 4, 5, 9, 10, 11}, {1, 3, 4, 5, 9, 10, 11}, {2, 3, 4, 5, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {2, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {0, 4, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {2, 4, 5, 7, 9, 10, 11}, {0, 4, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {0, 5, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {0, 4, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {2, 4, 5, 8, 9, 10, 11}, {3, 4, 5, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {3, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {3, 5, 6, 8, 9, 10, 11}

---

---

33. Graph1233:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {6,8}, {8,10}, {10,6}, {7,11}, {11,9}, {9,7}, {5,6}, {0,7}, {1,8}, {2,9}, {3,10}, {4,11}

• Randomly generated (generic) hyperplane:

  27*a + 80*b + 62*c + 21*d + 25*e + 3*f + 8*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : -40/27 : 0 : 0 : 0 : 40/27]

  [1 : -3/40 : 0 : -1 : 0 : 0 : 0]

  [1 : -1 : 0 : 13/24 : 37/24 : -37/12 : 37/24]

  [1 : -1 : 0 : 0 : 51/25 : -2 : 1]

  [0 : 0 : 1 : 1 : -77/25 : -2 : 0]

  [0 : 1 : -7/127 : -134/127 : -268/127 : 268/127 : -1]

  [0 : 1 : 0 : -50/43 : -93/43 : 93/43 : -1]

  [0 : 0 : 1 : 0 : 0 : 0 : -31/4]

  [1 : 0 : 0 : -49/43 : -6/43 : 6/43 : 0]

  [0 : 0 : 0 : 1 : 1 : -2 : -5]

  [1 : -49/50 : 0 : 0 : 99/50 : -99/50 : 49/50]

  [0 : 0 : 1 : -31/20 : -31/20 : 31/10 : 0]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 576 bases, 348 non-bases

  • circuits:

    • 2 circuits of size 3:

      {6, 8, 10}, {7, 9, 11}

    • 24 circuits of size 5:

      {0, 1, 2, 3, 4}, {0, 1, 2, 3, 5}, {0, 1, 2, 4, 5}, {0, 1, 3, 4, 5}, {0, 2, 3, 4, 5}, {1, 2, 3, 4, 5}, {1, 2, 3, 6, 8}, {0, 1, 5, 6, 8}, {3, 4, 5, 6, 8}, {0, 1, 2, 7, 9}, {2, 3, 4, 7, 9}, {0, 4, 5, 7, 9}, {1, 2, 3, 6, 10}, {0, 1, 5, 6, 10}, {3, 4, 5, 6, 10}, {1, 2, 3, 8, 10}, {0, 1, 5, 8, 10}, {3, 4, 5, 8, 10}, {0, 1, 2, 7, 11}, {2, 3, 4, 7, 11}, {0, 4, 5, 7, 11}, {0, 1, 2, 9, 11}, {2, 3, 4, 9, 11}, {0, 4, 5, 9, 11}

    • 36 circuits of size 6:

      {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 6, 8}, {0, 1, 3, 4, 7, 9}, {0, 1, 3, 5, 7, 9}, {0, 2, 3, 5, 7, 9}, {1, 2, 3, 5, 7, 9}, {1, 2, 4, 5, 7, 9}, {1, 3, 4, 5, 7, 9}, {0, 1, 2, 4, 6, 10}, {0, 1, 3, 4, 6, 10}, {0, 2, 3, 4, 6, 10}, {0, 2, 3, 5, 6, 10}, {0, 2, 4, 5, 6, 10}, {1, 2, 4, 5, 6, 10}, {0, 1, 2, 4, 8, 10}, {0, 1, 3, 4, 8, 10}, {0, 2, 3, 4, 8, 10}, {0, 2, 3, 5, 8, 10}, {0, 2, 4, 5, 8, 10}, {1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 7, 11}, {0, 1, 3, 5, 7, 11}, {0, 2, 3, 5, 7, 11}, {1, 2, 3, 5, 7, 11}, {1, 2, 4, 5, 7, 11}, {1, 3, 4, 5, 7, 11}, {0, 1, 3, 4, 9, 11}, {0, 1, 3, 5, 9, 11}, {0, 2, 3, 5, 9, 11}, {1, 2, 3, 5, 9, 11}, {1, 2, 4, 5, 9, 11}, {1, 3, 4, 5, 9, 11}

    • 126 circuits of size 7:

      {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {1, 2, 5, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {1, 4, 5, 6, 9, 10, 11}, {2, 4, 5, 6, 9, 10, 11}, {0, 1, 3, 8, 9, 10, 11}, {0, 2, 3, 8, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {1, 2, 4, 8, 9, 10, 11}, {0, 3, 4, 8, 9, 10, 11}, {1, 3, 4, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {0, 3, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {2, 3, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {2, 4, 5, 8, 9, 10, 11}

---

---

34. Graph1234:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {0,6}, {6,7}, {7,8}, {8,9}, {9,5}, {7,10}, {8,11}, {1,6}, {4,9}, {10,11}, {2,11}, {3,10}

• Randomly generated (generic) hyperplane:

  83*a + 16*b + 41*c + 52*d + 73*e + 10*f + 37*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 1 : 0 : -89/52 : 0 : -1 : 0]

  [1 : 0 : 0 : -119/52 : 1 : 0 : -1]

  [1 : 0 : 0 : -83/88 : -83/88 : 0 : 83/88]

  [1 : 0 : 0 : -83/125 : -83/125 : 0 : 0]

  [1 : 13/10 : -13/10 : -3/10 : -3/10 : -13/10 : 0]

  [1 : 1 : -89/41 : 0 : 0 : -1 : 0]

  [1 : 119/82 : 0 : -119/82 : -37/82 : -119/82 : 37/82]

  [0 : 1 : 0 : -1 : -1 : -109/27 : 109/27]

  [0 : 1 : 0 : -1 : -1 : 109/10 : 0]

  [0 : 1 : 119/41 : -1 : -1 : -1 : 0]

  [0 : 0 : 0 : 1 : 1 : 125/27 : -125/27]

  [0 : 0 : 0 : 1 : 1 : -44/5 : -1]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 594 bases, 330 non-bases

  • circuits:

    • 2 circuits of size 3:

      {0, 1, 6}, {4, 5, 9}

    • 2 circuits of size 4:

      {2, 3, 10, 11}, {7, 8, 10, 11}

    • 2 circuits of size 5:

      {2, 3, 7, 8, 10}, {2, 3, 7, 8, 11}

    • 96 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 7, 8}, {0, 1, 4, 5, 7, 8}, {2, 3, 4, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 9}, {0, 1, 2, 3, 5, 9}, {0, 2, 3, 4, 6, 9}, {1, 2, 3, 4, 6, 9}, {0, 2, 3, 5, 6, 9}, {1, 2, 3, 5, 6, 9}, {0, 1, 4, 7, 8, 9}, {2, 3, 4, 7, 8, 9}, {0, 1, 5, 7, 8, 9}, {2, 3, 5, 7, 8, 9}, {0, 4, 6, 7, 8, 9}, {1, 4, 6, 7, 8, 9}, {0, 5, 6, 7, 8, 9}, {1, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 7, 10}, {2, 3, 4, 5, 7, 10}, {0, 2, 3, 6, 7, 10}, {1, 2, 3, 6, 7, 10}, {0, 1, 2, 3, 8, 10}, {2, 3, 4, 5, 8, 10}, {0, 2, 3, 6, 8, 10}, {1, 2, 3, 6, 8, 10}, {0, 1, 2, 7, 8, 10}, {0, 1, 3, 7, 8, 10}, {2, 4, 5, 7, 8, 10}, {3, 4, 5, 7, 8, 10}, {0, 2, 6, 7, 8, 10}, {1, 2, 6, 7, 8, 10}, {0, 3, 6, 7, 8, 10}, {1, 3, 6, 7, 8, 10}, {2, 3, 4, 7, 9, 10}, {2, 3, 5, 7, 9, 10}, {2, 3, 4, 8, 9, 10}, {2, 3, 5, 8, 9, 10}, {2, 4, 7, 8, 9, 10}, {3, 4, 7, 8, 9, 10}, {2, 5, 7, 8, 9, 10}, {3, 5, 7, 8, 9, 10}, {0, 1, 2, 3, 7, 11}, {2, 3, 4, 5, 7, 11}, {0, 2, 3, 6, 7, 11}, {1, 2, 3, 6, 7, 11}, {0, 1, 2, 3, 8, 11}, {2, 3, 4, 5, 8, 11}, {0, 2, 3, 6, 8, 11}, {1, 2, 3, 6, 8, 11}, {0, 1, 2, 7, 8, 11}, {0, 1, 3, 7, 8, 11}, {2, 4, 5, 7, 8, 11}, {3, 4, 5, 7, 8, 11}, {0, 2, 6, 7, 8, 11}, {1, 2, 6, 7, 8, 11}, {0, 3, 6, 7, 8, 11}, {1, 3, 6, 7, 8, 11}, {2, 3, 4, 7, 9, 11}, {2, 3, 5, 7, 9, 11}, {2, 3, 4, 8, 9, 11}, {2, 3, 5, 8, 9, 11}, {2, 4, 7, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {2, 5, 7, 8, 9, 11}, {3, 5, 7, 8, 9, 11}, {0, 1, 2, 7, 10, 11}, {0, 1, 3, 7, 10, 11}, {2, 4, 5, 7, 10, 11}, {3, 4, 5, 7, 10, 11}, {0, 2, 6, 7, 10, 11}, {1, 2, 6, 7, 10, 11}, {0, 3, 6, 7, 10, 11}, {1, 3, 6, 7, 10, 11}, {0, 1, 2, 8, 10, 11}, {0, 1, 3, 8, 10, 11}, {2, 4, 5, 8, 10, 11}, {3, 4, 5, 8, 10, 11}, {0, 2, 6, 8, 10, 11}, {1, 2, 6, 8, 10, 11}, {0, 3, 6, 8, 10, 11}, {1, 3, 6, 8, 10, 11}, {2, 4, 7, 9, 10, 11}, {3, 4, 7, 9, 10, 11}, {2, 5, 7, 9, 10, 11}, {3, 5, 7, 9, 10, 11}, {2, 4, 8, 9, 10, 11}, {3, 4, 8, 9, 10, 11}, {2, 5, 8, 9, 10, 11}, {3, 5, 8, 9, 10, 11}

    • 108 circuits of size 7:

      {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 3, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {0, 1, 2, 4, 5, 7, 11}, {0, 1, 3, 4, 5, 7, 11}, {0, 2, 4, 5, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {0, 3, 4, 5, 6, 7, 11}, {1, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 3, 4, 5, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {0, 3, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 4, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 4, 5, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 4, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {0, 5, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}

---

---

35. Graph1235:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,5}, {5,6}, {6,1}, {4,9}, {9,10}, {10,3}, {6,7}, {7,8}, {8,5}, {11,8}, {9,11}, {0,11}, {10,7}

• Randomly generated (generic) hyperplane:

  83*a + 24*b + 74*c + 45*d + e + 65*f + 86*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 83/40 : 0 : 0 : 83/40 : -83/40 : 0]

  [1 : 0 : -83/10 : 0 : -83/10 : 83/10 : 0]

  [1 : 93/50 : -43/50 : 0 : 1 : -1 : 0]

  [0 : 1 : -12/37 : 0 : 0 : 0 : 0]

  [0 : 0 : 1 : -37/12 : 0 : -37/12 : 37/12]

  [0 : 0 : 0 : 1 : 6/5 : 11/5 : -11/5]

  [0 : 0 : 1 : 0 : 3/2 : -1/2 : -1/2]

  [0 : 0 : 1 : -6/13 : 6/13 : -20/13 : 7/13]

  [0 : 0 : 0 : 1 : -1 : 44/21 : -44/21]

  [0 : 1 : 61/50 : -61/50 : 1 : -61/50 : 11/50]

  [0 : 1 : 24/35 : -24/35 : 24/35 : -24/35 : 0]

  [0 : 1 : 0 : 0 : 1 : -61/21 : 40/21]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 684 bases, 240 non-bases

  • circuits:

    • 1 circuit of size 3:

      {0, 1, 2}

    • 2 circuits of size 4:

      {5, 6, 7, 8}, {3, 4, 9, 10}

    • 2 circuits of size 5:

      {4, 5, 8, 9, 11}, {7, 8, 9, 10, 11}

    • 86 circuits of size 6:

      {0, 1, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {3, 4, 5, 6, 7, 9}, {3, 4, 5, 6, 8, 9}, {3, 4, 5, 7, 8, 9}, {3, 4, 6, 7, 8, 9}, {0, 1, 3, 6, 7, 10}, {0, 2, 3, 6, 7, 10}, {1, 2, 3, 6, 7, 10}, {3, 4, 5, 6, 7, 10}, {3, 4, 5, 6, 8, 10}, {3, 4, 5, 7, 8, 10}, {3, 4, 6, 7, 8, 10}, {3, 5, 6, 7, 9, 10}, {4, 5, 6, 7, 9, 10}, {3, 5, 6, 8, 9, 10}, {4, 5, 6, 8, 9, 10}, {3, 5, 7, 8, 9, 10}, {4, 5, 7, 8, 9, 10}, {3, 6, 7, 8, 9, 10}, {4, 6, 7, 8, 9, 10}, {0, 1, 5, 6, 7, 11}, {0, 2, 5, 6, 7, 11}, {1, 2, 5, 6, 7, 11}, {3, 4, 5, 6, 7, 11}, {0, 1, 5, 6, 8, 11}, {0, 2, 5, 6, 8, 11}, {1, 2, 5, 6, 8, 11}, {3, 4, 5, 6, 8, 11}, {0, 1, 5, 7, 8, 11}, {0, 2, 5, 7, 8, 11}, {1, 2, 5, 7, 8, 11}, {3, 4, 5, 7, 8, 11}, {0, 1, 6, 7, 8, 11}, {0, 2, 6, 7, 8, 11}, {1, 2, 6, 7, 8, 11}, {3, 4, 6, 7, 8, 11}, {0, 1, 3, 4, 9, 11}, {0, 2, 3, 4, 9, 11}, {1, 2, 3, 4, 9, 11}, {3, 4, 5, 6, 9, 11}, {3, 4, 5, 7, 9, 11}, {3, 4, 6, 7, 9, 11}, {3, 5, 6, 7, 9, 11}, {4, 5, 6, 7, 9, 11}, {3, 4, 6, 8, 9, 11}, {3, 5, 6, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {3, 5, 7, 8, 9, 11}, {3, 6, 7, 8, 9, 11}, {4, 6, 7, 8, 9, 11}, {0, 1, 3, 4, 10, 11}, {0, 2, 3, 4, 10, 11}, {1, 2, 3, 4, 10, 11}, {3, 4, 5, 6, 10, 11}, {3, 4, 5, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {3, 5, 6, 7, 10, 11}, {4, 5, 6, 7, 10, 11}, {3, 4, 5, 8, 10, 11}, {3, 4, 6, 8, 10, 11}, {3, 5, 6, 8, 10, 11}, {4, 5, 6, 8, 10, 11}, {3, 4, 7, 8, 10, 11}, {3, 5, 7, 8, 10, 11}, {4, 5, 7, 8, 10, 11}, {3, 6, 7, 8, 10, 11}, {4, 6, 7, 8, 10, 11}, {0, 1, 3, 9, 10, 11}, {0, 2, 3, 9, 10, 11}, {1, 2, 3, 9, 10, 11}, {0, 1, 4, 9, 10, 11}, {0, 2, 4, 9, 10, 11}, {1, 2, 4, 9, 10, 11}, {3, 5, 6, 9, 10, 11}, {4, 5, 6, 9, 10, 11}, {3, 5, 7, 9, 10, 11}, {4, 5, 7, 9, 10, 11}, {3, 6, 7, 9, 10, 11}, {4, 6, 7, 9, 10, 11}, {5, 6, 7, 9, 10, 11}, {3, 5, 8, 9, 10, 11}, {3, 6, 8, 9, 10, 11}, {4, 6, 8, 9, 10, 11}, {5, 6, 8, 9, 10, 11}

    • 216 circuits of size 7:

      {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 3, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 7, 8}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {1, 2, 3, 4, 5, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 4, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {1, 2, 3, 4, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {1, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 4, 5, 6, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {1, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 1, 6, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {1, 2, 6, 7, 8, 9, 10}, {0, 1, 3, 4, 5, 7, 11}, {0, 2, 3, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 3, 4, 6, 7, 11}, {0, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 3, 7, 8, 9, 11}, {1, 2, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 4, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {1, 2, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 2, 6, 8, 9, 10, 11}

---

---

36. Graph1236:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,0}, {0,7}, {7,6}, {7,8}, {3,8}, {8,10}, {5,9}, {9,4}, {9,10}, {10,11}, {1,11}, {11,2}

• Randomly generated (generic) hyperplane:

  75*a + 27*b + 39*c + 95*d + 23*e + 5*f + 97*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : -75/4 : 0 : 0 : 75/4 : 0 : 0]

  [1 : 0 : 0 : 0 : 0 : -15 : 0]

  [1 : 0 : 0 : 0 : 0 : 43/23 : -20/23]

  [1 : 0 : 0 : -43/48 : 0 : 0 : 5/48]

  [1 : 0 : 10/67 : -57/67 : 0 : 0 : 0]

  [1 : 0 : 43/157 : -114/157 : -114/157 : 0 : 0]

  [1 : 43/122 : 0 : -79/122 : -1 : 0 : 0]

  [0 : 1 : 0 : -2/59 : -61/59 : 0 : 0]

  [0 : 0 : 0 : 1 : 96/37 : 0 : -59/37]

  [0 : 0 : 1 : 1 : -134/23 : 0 : 0]

  [0 : 0 : 0 : 0 : 1 : 0 : -23/97]

  [0 : 0 : 0 : 0 : 0 : 1 : -5/97]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 540 bases, 384 non-bases

  • circuits:

    • 3 circuits of size 3:

      {0, 6, 7}, {4, 5, 9}, {1, 2, 11}

    • 9 circuits of size 5:

      {1, 2, 3, 8, 10}, {3, 4, 5, 8, 10}, {0, 3, 6, 8, 10}, {0, 3, 7, 8, 10}, {3, 6, 7, 8, 10}, {3, 4, 8, 9, 10}, {3, 5, 8, 9, 10}, {1, 3, 8, 10, 11}, {2, 3, 8, 10, 11}

    • 81 circuits of size 6:

      {1, 2, 3, 4, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 3, 4, 5, 6, 8}, {0, 1, 2, 3, 7, 8}, {0, 3, 4, 5, 7, 8}, {1, 2, 3, 6, 7, 8}, {3, 4, 5, 6, 7, 8}, {1, 2, 3, 4, 8, 9}, {1, 2, 3, 5, 8, 9}, {0, 3, 4, 6, 8, 9}, {0, 3, 5, 6, 8, 9}, {0, 3, 4, 7, 8, 9}, {0, 3, 5, 7, 8, 9}, {3, 4, 6, 7, 8, 9}, {3, 5, 6, 7, 8, 9}, {1, 2, 3, 4, 5, 10}, {0, 1, 2, 3, 6, 10}, {0, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 7, 10}, {0, 3, 4, 5, 7, 10}, {1, 2, 3, 6, 7, 10}, {3, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 8, 10}, {0, 1, 2, 6, 8, 10}, {0, 4, 5, 6, 8, 10}, {0, 1, 2, 7, 8, 10}, {0, 4, 5, 7, 8, 10}, {1, 2, 6, 7, 8, 10}, {4, 5, 6, 7, 8, 10}, {1, 2, 3, 4, 9, 10}, {1, 2, 3, 5, 9, 10}, {0, 3, 4, 6, 9, 10}, {0, 3, 5, 6, 9, 10}, {0, 3, 4, 7, 9, 10}, {0, 3, 5, 7, 9, 10}, {3, 4, 6, 7, 9, 10}, {3, 5, 6, 7, 9, 10}, {1, 2, 4, 8, 9, 10}, {1, 2, 5, 8, 9, 10}, {0, 4, 6, 8, 9, 10}, {0, 5, 6, 8, 9, 10}, {0, 4, 7, 8, 9, 10}, {0, 5, 7, 8, 9, 10}, {4, 6, 7, 8, 9, 10}, {5, 6, 7, 8, 9, 10}, {1, 3, 4, 5, 8, 11}, {2, 3, 4, 5, 8, 11}, {0, 1, 3, 6, 8, 11}, {0, 2, 3, 6, 8, 11}, {0, 1, 3, 7, 8, 11}, {0, 2, 3, 7, 8, 11}, {1, 3, 6, 7, 8, 11}, {2, 3, 6, 7, 8, 11}, {1, 3, 4, 8, 9, 11}, {2, 3, 4, 8, 9, 11}, {1, 3, 5, 8, 9, 11}, {2, 3, 5, 8, 9, 11}, {1, 3, 4, 5, 10, 11}, {2, 3, 4, 5, 10, 11}, {0, 1, 3, 6, 10, 11}, {0, 2, 3, 6, 10, 11}, {0, 1, 3, 7, 10, 11}, {0, 2, 3, 7, 10, 11}, {1, 3, 6, 7, 10, 11}, {2, 3, 6, 7, 10, 11}, {1, 4, 5, 8, 10, 11}, {2, 4, 5, 8, 10, 11}, {0, 1, 6, 8, 10, 11}, {0, 2, 6, 8, 10, 11}, {0, 1, 7, 8, 10, 11}, {0, 2, 7, 8, 10, 11}, {1, 6, 7, 8, 10, 11}, {2, 6, 7, 8, 10, 11}, {1, 3, 4, 9, 10, 11}, {2, 3, 4, 9, 10, 11}, {1, 3, 5, 9, 10, 11}, {2, 3, 5, 9, 10, 11}, {1, 4, 8, 9, 10, 11}, {2, 4, 8, 9, 10, 11}, {1, 5, 8, 9, 10, 11}, {2, 5, 8, 9, 10, 11}

    • 81 circuits of size 7:

      {0, 1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 4, 5, 6, 8}, {0, 1, 2, 4, 5, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 6, 9}, {0, 1, 2, 3, 5, 6, 9}, {0, 1, 2, 3, 4, 7, 9}, {0, 1, 2, 3, 5, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 2, 5, 6, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 2, 5, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {1, 2, 5, 6, 7, 8, 9}, {0, 1, 2, 4, 5, 6, 10}, {0, 1, 2, 4, 5, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 1, 3, 4, 5, 6, 11}, {0, 2, 3, 4, 5, 6, 11}, {0, 1, 3, 4, 5, 7, 11}, {0, 2, 3, 4, 5, 7, 11}, {1, 3, 4, 5, 6, 7, 11}, {2, 3, 4, 5, 6, 7, 11}, {0, 1, 4, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {0, 1, 4, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}

---

---

37. Graph1237:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {0,8}, {8,1}, {5,6}, {6,4}, {3,7}, {7,2}, {8,9}, {9,10}, {11,9}, {6,10}, {11,10}, {11,7}

• Randomly generated (generic) hyperplane:

  16*a + 37*b + 86*c + 41*d + 67*e + 25*f + 74*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 0 : 0 : 1 : -25/74]

  [0 : 0 : 1 : 0 : 0 : 0 : -43/37]

  [0 : 1 : -37/86 : 0 : 0 : 0 : 0]

  [0 : 1 : 0 : -37/41 : 0 : 0 : 0]

  [1 : 0 : 0 : -48/41 : -1 : 1 : 1]

  [1 : 0 : 0 : 0 : -1 : 17/33 : 17/33]

  [1 : 0 : 0 : -51/58 : -1 : 51/58 : 51/58]

  [0 : 1 : 4/45 : -49/45 : 0 : 0 : 0]

  [0 : 0 : 1 : 0 : 0 : -12/25 : -1]

  [0 : 0 : 1 : 0 : 13/67 : -1 : -1]

  [0 : 0 : 0 : 1 : 58/67 : -1 : -1]

  [0 : 0 : 1 : -6 : -5 : 5 : 5]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 486 bases, 438 non-bases

  • circuits:

    • 4 circuits of size 3:

      {4, 5, 6}, {2, 3, 7}, {0, 1, 8}, {9, 10, 11}

    • 108 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 5, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {0, 3, 4, 5, 7, 8}, {1, 3, 4, 5, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {0, 3, 4, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {0, 1, 2, 3, 9, 10}, {0, 1, 4, 5, 9, 10}, {2, 3, 4, 5, 9, 10}, {0, 1, 4, 6, 9, 10}, {2, 3, 4, 6, 9, 10}, {0, 1, 5, 6, 9, 10}, {2, 3, 5, 6, 9, 10}, {0, 1, 2, 7, 9, 10}, {0, 1, 3, 7, 9, 10}, {2, 4, 5, 7, 9, 10}, {3, 4, 5, 7, 9, 10}, {2, 4, 6, 7, 9, 10}, {3, 4, 6, 7, 9, 10}, {2, 5, 6, 7, 9, 10}, {3, 5, 6, 7, 9, 10}, {0, 2, 3, 8, 9, 10}, {1, 2, 3, 8, 9, 10}, {0, 4, 5, 8, 9, 10}, {1, 4, 5, 8, 9, 10}, {0, 4, 6, 8, 9, 10}, {1, 4, 6, 8, 9, 10}, {0, 5, 6, 8, 9, 10}, {1, 5, 6, 8, 9, 10}, {0, 2, 7, 8, 9, 10}, {1, 2, 7, 8, 9, 10}, {0, 3, 7, 8, 9, 10}, {1, 3, 7, 8, 9, 10}, {0, 1, 2, 3, 9, 11}, {0, 1, 4, 5, 9, 11}, {2, 3, 4, 5, 9, 11}, {0, 1, 4, 6, 9, 11}, {2, 3, 4, 6, 9, 11}, {0, 1, 5, 6, 9, 11}, {2, 3, 5, 6, 9, 11}, {0, 1, 2, 7, 9, 11}, {0, 1, 3, 7, 9, 11}, {2, 4, 5, 7, 9, 11}, {3, 4, 5, 7, 9, 11}, {2, 4, 6, 7, 9, 11}, {3, 4, 6, 7, 9, 11}, {2, 5, 6, 7, 9, 11}, {3, 5, 6, 7, 9, 11}, {0, 2, 3, 8, 9, 11}, {1, 2, 3, 8, 9, 11}, {0, 4, 5, 8, 9, 11}, {1, 4, 5, 8, 9, 11}, {0, 4, 6, 8, 9, 11}, {1, 4, 6, 8, 9, 11}, {0, 5, 6, 8, 9, 11}, {1, 5, 6, 8, 9, 11}, {0, 2, 7, 8, 9, 11}, {1, 2, 7, 8, 9, 11}, {0, 3, 7, 8, 9, 11}, {1, 3, 7, 8, 9, 11}, {0, 1, 2, 3, 10, 11}, {0, 1, 4, 5, 10, 11}, {2, 3, 4, 5, 10, 11}, {0, 1, 4, 6, 10, 11}, {2, 3, 4, 6, 10, 11}, {0, 1, 5, 6, 10, 11}, {2, 3, 5, 6, 10, 11}, {0, 1, 2, 7, 10, 11}, {0, 1, 3, 7, 10, 11}, {2, 4, 5, 7, 10, 11}, {3, 4, 5, 7, 10, 11}, {2, 4, 6, 7, 10, 11}, {3, 4, 6, 7, 10, 11}, {2, 5, 6, 7, 10, 11}, {3, 5, 6, 7, 10, 11}, {0, 2, 3, 8, 10, 11}, {1, 2, 3, 8, 10, 11}, {0, 4, 5, 8, 10, 11}, {1, 4, 5, 8, 10, 11}, {0, 4, 6, 8, 10, 11}, {1, 4, 6, 8, 10, 11}, {0, 5, 6, 8, 10, 11}, {1, 5, 6, 8, 10, 11}, {0, 2, 7, 8, 10, 11}, {1, 2, 7, 8, 10, 11}, {0, 3, 7, 8, 10, 11}, {1, 3, 7, 8, 10, 11}

---

---

38. Graph1238:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,0}, {0,4}, {1,6}, {3,7}, {2,9}, {10,5}, {8,11}, {9,10}, {10,11}, {11,9}

• Randomly generated (generic) hyperplane:

  24*a + 15*b + 40*c + 83*d + 41*e + 33*f + 46*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 1 : -13 : 13 : 0 : 0 : -13]

  [1 : 1 : 0 : 0 : -39/41 : 0 : 0]

  [0 : 0 : 0 : 1 : -83/41 : 0 : 0]

  [0 : 1 : -1 : 63/83 : 1 : -1 : -1]

  [1 : -4/5 : 4/5 : -4/5 : -9/5 : 9/5 : 4/5]

  [1 : 0 : 0 : 0 : -1 : 17/33 : 0]

  [1 : 17/15 : 0 : 0 : -1 : 0 : 0]

  [0 : 1 : -5/26 : 0 : 5/26 : -5/26 : -5/26]

  [0 : 0 : 1 : -26/25 : 1/25 : -1/25 : 1]

  [0 : 0 : 0 : 1 : 2/19 : -21/19 : -21/19]

  [0 : 0 : 0 : 1 : 0 : -37/33 : -1]

  [0 : 0 : 0 : 1 : 37/38 : -37/78 : -75/38]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 720 bases, 204 non-bases

  • circuits:

    • 1 circuit of size 3:

      {9, 10, 11}

    • 6 circuits of size 5:

      {0, 1, 2, 3, 4}, {0, 1, 4, 5, 6}, {1, 2, 3, 6, 7}, {3, 4, 5, 6, 7}, {0, 3, 4, 7, 8}, {0, 1, 6, 7, 8}

    • 78 circuits of size 6:

      {0, 1, 2, 3, 5, 6}, {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 5, 7}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 7}, {1, 2, 3, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {0, 1, 2, 3, 5, 8}, {0, 1, 2, 4, 5, 8}, {0, 1, 3, 4, 5, 8}, {0, 2, 3, 4, 5, 8}, {1, 2, 3, 4, 5, 8}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 4, 6, 8}, {0, 1, 3, 4, 6, 8}, {0, 2, 3, 4, 6, 8}, {1, 2, 3, 4, 6, 8}, {0, 1, 2, 5, 6, 8}, {0, 1, 3, 5, 6, 8}, {0, 2, 3, 5, 6, 8}, {1, 2, 3, 5, 6, 8}, {0, 2, 4, 5, 6, 8}, {1, 2, 4, 5, 6, 8}, {0, 3, 4, 5, 6, 8}, {1, 3, 4, 5, 6, 8}, {2, 3, 4, 5, 6, 8}, {0, 1, 2, 3, 7, 8}, {0, 1, 2, 4, 7, 8}, {1, 2, 3, 4, 7, 8}, {0, 1, 2, 5, 7, 8}, {0, 1, 3, 5, 7, 8}, {0, 2, 3, 5, 7, 8}, {1, 2, 3, 5, 7, 8}, {0, 1, 4, 5, 7, 8}, {0, 2, 4, 5, 7, 8}, {1, 2, 4, 5, 7, 8}, {1, 3, 4, 5, 7, 8}, {2, 3, 4, 5, 7, 8}, {0, 2, 3, 6, 7, 8}, {0, 2, 4, 6, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 3, 4, 6, 7, 8}, {2, 3, 4, 6, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 5, 6, 7, 8}, {0, 3, 5, 6, 7, 8}, {1, 3, 5, 6, 7, 8}, {2, 3, 5, 6, 7, 8}, {0, 4, 5, 6, 7, 8}, {1, 4, 5, 6, 7, 8}, {2, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 9, 10}, {1, 2, 5, 6, 9, 10}, {0, 1, 2, 8, 9, 10}, {0, 4, 5, 8, 9, 10}, {2, 3, 7, 8, 9, 10}, {5, 6, 7, 8, 9, 10}, {2, 3, 4, 5, 9, 11}, {1, 2, 5, 6, 9, 11}, {0, 1, 2, 8, 9, 11}, {0, 4, 5, 8, 9, 11}, {2, 3, 7, 8, 9, 11}, {5, 6, 7, 8, 9, 11}, {2, 3, 4, 5, 10, 11}, {1, 2, 5, 6, 10, 11}, {0, 1, 2, 8, 10, 11}, {0, 4, 5, 8, 10, 11}, {2, 3, 7, 8, 10, 11}, {5, 6, 7, 8, 10, 11}

    • 270 circuits of size 7:

      {0, 1, 2, 3, 5, 9, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 1, 2, 3, 6, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 3, 7, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 2, 6, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 4, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 2, 3, 4, 8, 9, 10}, {1, 2, 3, 4, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {3, 4, 5, 6, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {1, 2, 6, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {1, 3, 6, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 3, 7, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 4, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 2, 3, 4, 8, 9, 11}, {1, 2, 3, 4, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {3, 4, 5, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {3, 4, 5, 7, 8, 9, 11}, {0, 2, 6, 7, 8, 9, 11}, {1, 2, 6, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 3, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {0, 3, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 3, 7, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 3, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {2, 3, 4, 6, 7, 10, 11}, {0, 1, 5, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {0, 4, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {3, 4, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {3, 4, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {0, 4, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {3, 4, 6, 7, 8, 10, 11}

---

---

39. Graph1239:

• Edges of graph:

  {0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,5}, {5,6}, {6,1}, {5,11}, {11,4}, {0,10}, {10,11}, {10,8}, {3,7}, {7,8}, {8,9}, {9,6}, {7,9}

• Randomly generated (generic) hyperplane:

  33*a + 8*b + 51*c + 6*d + 49*e + 34*f + 43*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : -1/28 : 0 : -27/28 : 0]

  [1 : -27/14 : 0 : -41/14 : 0 : 0 : 0]

  [1 : 1/42 : 0 : 0 : 0 : -41/42 : 0]

  [0 : 1 : 0 : 0 : 0 : 5/11 : -6/11]

  [0 : 1 : 35/94 : 0 : 0 : 0 : -59/94]

  [0 : 1 : 29/88 : 59/88 : 0 : 0 : -59/88]

  [0 : 1 : 0 : 1 : 0 : 0 : -14/43]

  [0 : 0 : 0 : 0 : 1 : -92/77 : -15/77]

  [0 : 0 : 0 : 0 : 1 : -46/17 : 1]

  [0 : 0 : 0 : 0 : 1 : -1 : -15/43]

  [0 : 0 : 0 : 1 : 0 : -3/17 : 0]

  [0 : 0 : 1 : -47/3 : 0 : 0 : 1]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 540 bases, 384 non-bases

  • circuits:

    • 3 circuits of size 3:

      {0, 1, 2}, {7, 8, 9}, {4, 5, 11}

    • 9 circuits of size 5:

      {0, 1, 3, 6, 10}, {0, 2, 3, 6, 10}, {1, 2, 3, 6, 10}, {3, 4, 5, 6, 10}, {3, 6, 7, 8, 10}, {3, 6, 7, 9, 10}, {3, 6, 8, 9, 10}, {3, 4, 6, 10, 11}, {3, 5, 6, 10, 11}

    • 81 circuits of size 6:

      {0, 1, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {3, 4, 5, 6, 7, 8}, {0, 1, 3, 6, 7, 9}, {0, 2, 3, 6, 7, 9}, {1, 2, 3, 6, 7, 9}, {3, 4, 5, 6, 7, 9}, {0, 1, 3, 6, 8, 9}, {0, 2, 3, 6, 8, 9}, {1, 2, 3, 6, 8, 9}, {3, 4, 5, 6, 8, 9}, {0, 1, 3, 4, 5, 10}, {0, 2, 3, 4, 5, 10}, {1, 2, 3, 4, 5, 10}, {0, 1, 4, 5, 6, 10}, {0, 2, 4, 5, 6, 10}, {1, 2, 4, 5, 6, 10}, {0, 1, 3, 7, 8, 10}, {0, 2, 3, 7, 8, 10}, {1, 2, 3, 7, 8, 10}, {3, 4, 5, 7, 8, 10}, {0, 1, 6, 7, 8, 10}, {0, 2, 6, 7, 8, 10}, {1, 2, 6, 7, 8, 10}, {4, 5, 6, 7, 8, 10}, {0, 1, 3, 7, 9, 10}, {0, 2, 3, 7, 9, 10}, {1, 2, 3, 7, 9, 10}, {3, 4, 5, 7, 9, 10}, {0, 1, 6, 7, 9, 10}, {0, 2, 6, 7, 9, 10}, {1, 2, 6, 7, 9, 10}, {4, 5, 6, 7, 9, 10}, {0, 1, 3, 8, 9, 10}, {0, 2, 3, 8, 9, 10}, {1, 2, 3, 8, 9, 10}, {3, 4, 5, 8, 9, 10}, {0, 1, 6, 8, 9, 10}, {0, 2, 6, 8, 9, 10}, {1, 2, 6, 8, 9, 10}, {4, 5, 6, 8, 9, 10}, {0, 1, 3, 4, 6, 11}, {0, 2, 3, 4, 6, 11}, {1, 2, 3, 4, 6, 11}, {0, 1, 3, 5, 6, 11}, {0, 2, 3, 5, 6, 11}, {1, 2, 3, 5, 6, 11}, {3, 4, 6, 7, 8, 11}, {3, 5, 6, 7, 8, 11}, {3, 4, 6, 7, 9, 11}, {3, 5, 6, 7, 9, 11}, {3, 4, 6, 8, 9, 11}, {3, 5, 6, 8, 9, 11}, {0, 1, 3, 4, 10, 11}, {0, 2, 3, 4, 10, 11}, {1, 2, 3, 4, 10, 11}, {0, 1, 3, 5, 10, 11}, {0, 2, 3, 5, 10, 11}, {1, 2, 3, 5, 10, 11}, {0, 1, 4, 6, 10, 11}, {0, 2, 4, 6, 10, 11}, {1, 2, 4, 6, 10, 11}, {0, 1, 5, 6, 10, 11}, {0, 2, 5, 6, 10, 11}, {1, 2, 5, 6, 10, 11}, {3, 4, 7, 8, 10, 11}, {3, 5, 7, 8, 10, 11}, {4, 6, 7, 8, 10, 11}, {5, 6, 7, 8, 10, 11}, {3, 4, 7, 9, 10, 11}, {3, 5, 7, 9, 10, 11}, {4, 6, 7, 9, 10, 11}, {5, 6, 7, 9, 10, 11}, {3, 4, 8, 9, 10, 11}, {3, 5, 8, 9, 10, 11}, {4, 6, 8, 9, 10, 11}, {5, 6, 8, 9, 10, 11}

    • 81 circuits of size 7:

      {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 4, 5, 6, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {1, 2, 3, 4, 5, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 1, 5, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 2, 3, 4, 8, 9, 11}, {1, 2, 3, 4, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {1, 2, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}

---

---

40. Graph1240:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,6}, {0,7}, {1,8}, {2,9}, {3,10}, {4,11}, {5,6}

• Randomly generated (generic) hyperplane:

  3*a + 90*b + 69*c + 47*d + 45*e + 61*f + 70*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 1 : -47/45 : 0 : 0]

  [1 : 0 : 0 : -3/47 : 0 : 0 : 0]

  [1 : -1/30 : 0 : 0 : 0 : 0 : 0]

  [0 : 1 : -30/23 : 0 : 0 : 0 : 0]

  [0 : 0 : 1 : -69/83 : -69/83 : -69/83 : 69/83]

  [0 : 0 : 0 : 1 : 1 : 92/9 : -92/9]

  [0 : 0 : 0 : 0 : 0 : 1 : -61/70]

  [0 : 0 : 0 : 0 : 1 : -45/61 : 0]

  [1 : 0 : 0 : -1 : 22/53 : 22/53 : 0]

  [1 : -50/21 : 0 : 29/21 : 29/21 : 29/21 : 0]

  [0 : 1 : -3/4 : -1/4 : -1/4 : -1/4 : 0]

  [0 : 0 : 1 : -1 : -1 : -1 : 6/5]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 664 bases, 260 non-bases

  • circuits:

    • 6 circuits of size 4:

      {0, 5, 6, 7}, {0, 1, 7, 8}, {1, 2, 8, 9}, {2, 3, 9, 10}, {4, 5, 6, 11}, {3, 4, 10, 11}

    • 12 circuits of size 5:

      {0, 1, 5, 6, 8}, {1, 5, 6, 7, 8}, {0, 1, 2, 7, 9}, {0, 2, 7, 8, 9}, {3, 4, 5, 6, 10}, {1, 2, 3, 8, 10}, {1, 3, 8, 9, 10}, {0, 4, 5, 7, 11}, {0, 4, 6, 7, 11}, {2, 3, 4, 9, 11}, {3, 5, 6, 10, 11}, {2, 4, 9, 10, 11}

    • 26 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 5, 6, 9}, {2, 3, 4, 5, 6, 9}, {1, 2, 5, 6, 7, 9}, {0, 2, 5, 6, 8, 9}, {2, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 7, 10}, {0, 3, 4, 5, 7, 10}, {0, 3, 4, 6, 7, 10}, {0, 2, 3, 7, 8, 10}, {2, 4, 5, 6, 9, 10}, {0, 1, 3, 7, 9, 10}, {0, 3, 7, 8, 9, 10}, {1, 2, 3, 4, 8, 11}, {0, 1, 4, 5, 8, 11}, {0, 1, 4, 6, 8, 11}, {1, 4, 5, 7, 8, 11}, {1, 4, 6, 7, 8, 11}, {2, 3, 5, 6, 9, 11}, {1, 3, 4, 8, 9, 11}, {0, 3, 5, 7, 10, 11}, {0, 3, 6, 7, 10, 11}, {1, 2, 4, 8, 10, 11}, {2, 5, 6, 9, 10, 11}, {1, 4, 8, 9, 10, 11}, {6, 7, 8, 9, 10, 11}

    • 228 circuits of size 7:

      {0, 1, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 6, 9}, {0, 1, 3, 4, 5, 6, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 1, 2, 4, 5, 6, 10}, {0, 1, 2, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {4, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 1, 2, 3, 4, 7, 11}, {0, 1, 2, 3, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {3, 4, 5, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {0, 3, 5, 8, 9, 10, 11}, {0, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}, {3, 5, 7, 8, 9, 10, 11}, {4, 5, 7, 8, 9, 10, 11}

---

---

41. Graph1241:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,6}, {0,7}, {1,8}, {2,10}, {3,9}, {4,11}, {5,6}

• Randomly generated (generic) hyperplane:

  69*a + 17*b + 63*c + 67*d + 19*e + 52*f + 23*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : -44/43 : -1/43 : 0 : 0]

  [1 : -88/17 : 0 : 0 : 1 : 0 : 0]

  [0 : 1 : 17/8 : 0 : -17/8 : -17/8 : 0]

  [0 : 1 : 1 : -9/67 : -1 : -1 : 0]

  [0 : 0 : 0 : 1 : -67/48 : -67/48 : 67/48]

  [0 : 0 : 0 : 1 : -19/24 : -43/24 : 43/24]

  [0 : 0 : 0 : 1 : 0 : -1 : -15/23]

  [1 : 0 : 0 : -17/15 : 0 : 2/15 : 0]

  [1 : 17/54 : 0 : 0 : -17/54 : -17/54 : 0]

  [0 : 1 : -27/2 : 27/2 : -1 : -1 : 0]

  [0 : 0 : 1 : -2 : 1 : 1 : 0]

  [0 : 0 : 0 : 1 : -1 : -1 : 4/23]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 714 bases, 210 non-bases

  • circuits:

    • 4 circuits of size 4:

      {0, 5, 6, 7}, {0, 1, 7, 8}, {2, 3, 9, 10}, {4, 5, 6, 11}

    • 12 circuits of size 5:

      {0, 1, 5, 6, 8}, {1, 5, 6, 7, 8}, {1, 2, 3, 8, 9}, {1, 2, 3, 8, 10}, {1, 2, 8, 9, 10}, {1, 3, 8, 9, 10}, {0, 4, 5, 7, 11}, {0, 4, 6, 7, 11}, {2, 3, 4, 9, 11}, {2, 3, 4, 10, 11}, {2, 4, 9, 10, 11}, {3, 4, 9, 10, 11}

    • 28 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {2, 3, 4, 5, 6, 9}, {0, 1, 2, 3, 7, 9}, {0, 2, 3, 7, 8, 9}, {2, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 7, 10}, {0, 2, 3, 7, 8, 10}, {2, 4, 5, 6, 9, 10}, {3, 4, 5, 6, 9, 10}, {0, 1, 2, 7, 9, 10}, {0, 1, 3, 7, 9, 10}, {0, 2, 7, 8, 9, 10}, {0, 3, 7, 8, 9, 10}, {1, 2, 3, 4, 8, 11}, {0, 1, 4, 5, 8, 11}, {0, 1, 4, 6, 8, 11}, {1, 4, 5, 7, 8, 11}, {1, 4, 6, 7, 8, 11}, {2, 3, 5, 6, 9, 11}, {1, 2, 4, 8, 9, 11}, {1, 3, 4, 8, 9, 11}, {2, 3, 5, 6, 10, 11}, {1, 2, 4, 8, 10, 11}, {1, 3, 4, 8, 10, 11}, {2, 5, 6, 9, 10, 11}, {3, 5, 6, 9, 10, 11}, {1, 4, 8, 9, 10, 11}, {6, 7, 8, 9, 10, 11}

    • 300 circuits of size 7:

      {0, 1, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 6, 9}, {0, 1, 2, 3, 5, 6, 9}, {0, 1, 2, 4, 5, 6, 9}, {0, 1, 3, 4, 5, 6, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 1, 2, 4, 5, 6, 10}, {0, 1, 3, 4, 5, 6, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {4, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 1, 2, 3, 4, 7, 11}, {0, 1, 2, 3, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {3, 4, 5, 7, 8, 9, 11}, {0, 2, 6, 7, 8, 9, 11}, {1, 2, 6, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 3, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {0, 3, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {3, 4, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {3, 4, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {3, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {0, 3, 5, 8, 9, 10, 11}, {0, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}, {3, 5, 7, 8, 9, 10, 11}, {4, 5, 7, 8, 9, 10, 11}

---

---

42. Graph1242:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,6}, {0,7}, {1,8}, {2,10}, {3,9}, {4,6}, {5,11}

• Randomly generated (generic) hyperplane:

  65*a + 30*b + 7*c + 60*d + 15*e + 4*f + 74*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : -1 : 0 : -58/15 : 0 : 0]

  [0 : 1 : -1 : 0 : -19/15 : -1 : 0]

  [0 : 1 : -15/17 : -2/17 : -15/17 : -15/17 : 0]

  [0 : 1 : 30/7 : -1 : 0 : 0 : 0]

  [1 : 0 : -10/7 : 0 : 1 : 1 : -1]

  [1 : 0 : -1 : 0 : 58/55 : 58/55 : -58/55]

  [1 : 0 : 0 : 0 : 1 : 1 : -42/37]

  [1 : 0 : -84/11 : 0 : 1 : -73/11 : 0]

  [0 : 1 : -30/11 : 0 : 0 : -30/11 : 0]

  [0 : 1 : 30/53 : -30/53 : 0 : 0 : 0]

  [0 : 0 : 1 : -1 : 53/19 : 53/19 : 0]

  [0 : 0 : 0 : 0 : 1 : 1 : -19/74]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 756 bases, 168 non-bases

  • circuits:

    • 3 circuits of size 4:

      {0, 1, 7, 8}, {2, 3, 9, 10}, {4, 5, 6, 11}

    • 8 circuits of size 5:

      {0, 4, 5, 6, 7}, {1, 2, 3, 8, 9}, {1, 2, 3, 8, 10}, {1, 2, 8, 9, 10}, {1, 3, 8, 9, 10}, {0, 4, 5, 7, 11}, {0, 4, 6, 7, 11}, {0, 5, 6, 7, 11}

    • 36 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 4, 5, 6, 8}, {1, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 9}, {0, 1, 2, 3, 7, 9}, {0, 2, 3, 7, 8, 9}, {3, 4, 6, 7, 8, 9}, {2, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 7, 10}, {0, 2, 3, 7, 8, 10}, {2, 4, 5, 6, 9, 10}, {3, 4, 5, 6, 9, 10}, {0, 1, 2, 7, 9, 10}, {0, 1, 3, 7, 9, 10}, {0, 2, 7, 8, 9, 10}, {0, 3, 7, 8, 9, 10}, {0, 1, 4, 5, 8, 11}, {0, 1, 4, 6, 8, 11}, {0, 1, 5, 6, 8, 11}, {1, 4, 5, 7, 8, 11}, {1, 4, 6, 7, 8, 11}, {1, 5, 6, 7, 8, 11}, {2, 3, 4, 5, 9, 11}, {2, 3, 4, 6, 9, 11}, {2, 3, 5, 6, 9, 11}, {0, 1, 2, 5, 10, 11}, {2, 3, 4, 5, 10, 11}, {2, 3, 4, 6, 10, 11}, {2, 3, 5, 6, 10, 11}, {2, 4, 5, 9, 10, 11}, {3, 4, 5, 9, 10, 11}, {2, 4, 6, 9, 10, 11}, {3, 4, 6, 9, 10, 11}, {2, 5, 6, 9, 10, 11}, {3, 5, 6, 9, 10, 11}, {6, 7, 8, 9, 10, 11}

    • 360 circuits of size 7:

      {0, 1, 2, 3, 4, 6, 7}, {0, 1, 2, 3, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 4, 6, 8}, {0, 1, 2, 3, 5, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 7, 8}, {0, 2, 3, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 6, 9}, {0, 1, 2, 3, 5, 6, 9}, {0, 1, 2, 4, 5, 6, 9}, {0, 1, 3, 4, 5, 6, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {0, 1, 2, 5, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {0, 1, 2, 5, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {1, 2, 5, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 1, 2, 4, 5, 6, 10}, {0, 1, 3, 4, 5, 6, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 1, 2, 5, 6, 7, 10}, {0, 1, 3, 5, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {0, 5, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {4, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 1, 2, 3, 4, 7, 11}, {0, 1, 2, 3, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 2, 3, 4, 8, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 4, 9, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 2, 3, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {2, 3, 4, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {3, 4, 5, 7, 8, 9, 11}, {0, 2, 6, 7, 8, 9, 11}, {1, 2, 6, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 4, 10, 11}, {0, 1, 3, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 3, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {2, 3, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {3, 4, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {3, 4, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {3, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 3, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {0, 3, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {0, 3, 5, 8, 9, 10, 11}, {0, 4, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {2, 4, 7, 8, 9, 10, 11}, {3, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}, {3, 5, 7, 8, 9, 10, 11}, {4, 5, 7, 8, 9, 10, 11}

---

---

43. Graph1243:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {5,6}, {6,7}, {7,9}, {9,10}, {10,11}, {11,5}, {10,8}, {8,7}, {3,9}, {2,8}, {4,11}, {0,5}, {1,6}

• Randomly generated (generic) hyperplane:

  93*a + 82*b + 86*c + 99*d + 18*e + 48*f + 47*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : 0 : 0 : 1 : -53/48 : -1]

  [1 : 0 : 0 : 0 : 0 : -31/16 : 0]

  [1 : 0 : 0 : -31/33 : 0 : 0 : 0]

  [0 : 0 : 0 : 1 : 0 : 0 : -99/47]

  [0 : 1 : 0 : 0 : 1 : 0 : -100/47]

  [0 : 1 : -1/23 : 0 : 24/23 : -1 : -24/23]

  [1 : 0 : -9/23 : 0 : 9/23 : -1 : -9/23]

  [1 : 0 : -1 : 35/11 : 46/11 : -46/11 : -46/11]

  [1 : 0 : 0 : -8/11 : 3/11 : -3/11 : -3/11]

  [1 : 0 : -1 : 25/13 : 2 : -2 : -38/13]

  [1 : 0 : -4/29 : 0 : 33/29 : -33/29 : -1]

  [0 : 1 : -3/58 : 0 : 61/58 : -3/58 : -2]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 744 bases, 180 non-bases

  • circuits:

    • 3 circuits of size 4:

      {0, 1, 5, 6}, {7, 8, 9, 10}, {0, 4, 5, 11}

    • 9 circuits of size 5:

      {0, 1, 2, 3, 4}, {1, 2, 6, 7, 8}, {2, 3, 7, 8, 9}, {2, 3, 7, 8, 10}, {2, 3, 7, 9, 10}, {2, 3, 8, 9, 10}, {0, 1, 4, 6, 11}, {1, 4, 5, 6, 11}, {3, 4, 9, 10, 11}

    • 40 circuits of size 6:

      {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {0, 1, 2, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {1, 2, 3, 6, 7, 9}, {1, 2, 3, 6, 8, 9}, {1, 3, 6, 7, 8, 9}, {1, 2, 3, 6, 7, 10}, {1, 2, 3, 6, 8, 10}, {1, 3, 6, 7, 8, 10}, {0, 3, 4, 5, 9, 10}, {1, 2, 3, 6, 9, 10}, {1, 2, 6, 7, 9, 10}, {1, 3, 6, 7, 9, 10}, {1, 2, 6, 8, 9, 10}, {1, 3, 6, 8, 9, 10}, {0, 1, 2, 3, 5, 11}, {1, 2, 3, 4, 5, 11}, {0, 1, 2, 3, 6, 11}, {0, 2, 3, 4, 6, 11}, {1, 2, 3, 4, 6, 11}, {0, 2, 3, 5, 6, 11}, {1, 2, 3, 5, 6, 11}, {2, 3, 4, 5, 6, 11}, {2, 3, 4, 7, 8, 11}, {2, 3, 4, 7, 9, 11}, {2, 3, 4, 8, 9, 11}, {2, 4, 7, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {5, 6, 7, 8, 9, 11}, {2, 3, 4, 7, 10, 11}, {2, 3, 4, 8, 10, 11}, {2, 4, 7, 8, 10, 11}, {3, 4, 7, 8, 10, 11}, {5, 6, 7, 8, 10, 11}, {0, 3, 5, 9, 10, 11}, {2, 4, 7, 9, 10, 11}, {5, 6, 7, 9, 10, 11}, {2, 4, 8, 9, 10, 11}, {5, 6, 8, 9, 10, 11}

    • 320 circuits of size 7:

      {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 3, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 5, 7, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 3, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 3, 5, 8, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {1, 2, 3, 4, 5, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {0, 4, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 5, 7, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 3, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {2, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {0, 4, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 1, 2, 4, 5, 9, 10}, {1, 2, 3, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {2, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {0, 4, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {3, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {3, 4, 5, 6, 8, 9, 10}, {0, 1, 2, 3, 7, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {3, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 7, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {3, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 3, 8, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {3, 4, 5, 6, 8, 9, 11}, {0, 1, 2, 7, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {0, 1, 6, 7, 8, 9, 11}, {0, 2, 6, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 7, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {3, 4, 5, 6, 7, 10, 11}, {0, 1, 2, 3, 8, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {3, 4, 5, 6, 8, 10, 11}, {0, 1, 2, 7, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {0, 1, 6, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {0, 4, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {0, 1, 2, 3, 9, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {2, 4, 5, 6, 9, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {0, 4, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {0, 1, 2, 8, 9, 10, 11}, {0, 1, 3, 8, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}

---

---

44. Graph1244:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,0}, {0,9}, {3,9}, {2,8}, {8,9}, {7,11}, {4,11}, {6,8}, {5,10}, {11,10}, {10,1}

• Randomly generated (generic) hyperplane:

  69*a + 71*b + 8*c + 40*d + 11*e + 74*f + 75*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 3/4 : 0 : 0 : 0 : -1]

  [1 : 0 : 0 : 0 : 0 : 0 : -23/25]

  [1 : 23/11 : 0 : -23/11 : 23/11 : 0 : -23/11]

  [1 : -18/11 : -1 : 7/11 : -18/11 : 0 : 7/11]

  [1 : -1 : -1 : 0 : 10/11 : 0 : 0]

  [1 : -1 : -1 : 0 : 1 : 1 : -1]

  [1 : -1 : -31/41 : 0 : -1 : -31/41 : 1]

  [0 : 0 : 1 : 0 : 0 : -4/37 : 0]

  [1 : -1 : 0 : -31/20 : -1 : 0 : 1]

  [1 : 0 : -1 : 7/20 : 0 : 0 : -1]

  [0 : 0 : 0 : 0 : 1 : 1 : -17/15]

  [0 : 0 : 0 : 0 : 1 : -11/74 : 0]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 774 bases, 150 non-bases

  • circuits:

    • 2 circuits of size 4:

      {2, 3, 8, 9}, {4, 5, 10, 11}

    • 10 circuits of size 5:

      {0, 1, 2, 3, 8}, {0, 1, 2, 3, 9}, {0, 1, 2, 8, 9}, {0, 1, 3, 8, 9}, {0, 6, 7, 8, 9}, {4, 5, 6, 7, 10}, {4, 5, 6, 7, 11}, {0, 1, 7, 10, 11}, {4, 6, 7, 10, 11}, {5, 6, 7, 10, 11}

    • 32 circuits of size 6:

      {0, 1, 2, 3, 6, 7}, {0, 1, 4, 5, 6, 7}, {2, 3, 4, 5, 6, 8}, {0, 1, 2, 6, 7, 8}, {0, 1, 3, 6, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {2, 3, 4, 5, 6, 9}, {0, 1, 2, 6, 7, 9}, {0, 1, 3, 6, 7, 9}, {0, 2, 3, 6, 7, 9}, {1, 2, 3, 6, 7, 9}, {2, 4, 5, 6, 8, 9}, {3, 4, 5, 6, 8, 9}, {1, 2, 6, 7, 8, 9}, {1, 3, 6, 7, 8, 9}, {1, 2, 3, 4, 5, 10}, {0, 1, 4, 5, 6, 10}, {0, 1, 4, 5, 7, 10}, {0, 1, 4, 6, 7, 10}, {0, 1, 5, 6, 7, 10}, {1, 2, 5, 6, 8, 10}, {1, 2, 3, 4, 5, 11}, {0, 1, 4, 5, 6, 11}, {0, 1, 4, 5, 7, 11}, {0, 1, 4, 6, 7, 11}, {0, 1, 5, 6, 7, 11}, {0, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 10, 11}, {1, 2, 3, 5, 10, 11}, {0, 1, 4, 6, 10, 11}, {0, 1, 5, 6, 10, 11}

    • 384 circuits of size 7:

      {0, 1, 2, 3, 4, 5, 6}, {0, 1, 2, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 4, 5, 6, 8}, {0, 1, 3, 4, 5, 6, 8}, {0, 1, 2, 4, 5, 7, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 4, 5, 6, 9}, {0, 1, 3, 4, 5, 6, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 3, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 2, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 4, 7, 10}, {0, 1, 2, 3, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 2, 5, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 2, 3, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {2, 3, 4, 5, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 2, 3, 4, 5, 6, 11}, {0, 1, 2, 3, 4, 7, 11}, {0, 1, 2, 3, 5, 7, 11}, {0, 2, 3, 4, 5, 7, 11}, {0, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 2, 5, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 2, 3, 4, 5, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 4, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {0, 4, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {3, 4, 5, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {1, 2, 3, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {2, 3, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 2, 3, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {2, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {0, 2, 3, 7, 9, 10, 11}, {1, 2, 3, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {2, 3, 4, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 3, 6, 7, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {1, 2, 4, 8, 9, 10, 11}, {0, 3, 4, 8, 9, 10, 11}, {1, 3, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {0, 3, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {3, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {3, 5, 6, 8, 9, 10, 11}, {0, 2, 7, 8, 9, 10, 11}, {1, 2, 7, 8, 9, 10, 11}, {0, 3, 7, 8, 9, 10, 11}, {1, 3, 7, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {2, 4, 7, 8, 9, 10, 11}, {3, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}, {3, 5, 7, 8, 9, 10, 11}, {1, 6, 7, 8, 9, 10, 11}, {2, 6, 7, 8, 9, 10, 11}, {3, 6, 7, 8, 9, 10, 11}

---

---

45. Graph1245:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,6}, {11,8}, {0,6}, {2,7}, {3,9}, {5,10}, {1,4}

• Randomly generated (generic) hyperplane:

  61*a + b + 78*c + 99*d + 2*e + 60*f + 27*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 86/59 : 0 : 0 : -1 : -86/59 : 1]

  [0 : 1 : 59/78 : 0 : 0 : -1 : 0]

  [0 : 0 : 1 : -26/33 : 0 : 0 : 0]

  [0 : 1 : 1 : -106/99 : 0 : 0 : 1]

  [0 : 1 : 1 : 0 : 0 : -106/87 : -19/87]

  [1 : 0 : 0 : 0 : -1 : -86/87 : 1/87]

  [1 : 213/77 : 145/77 : -145/77 : 68/77 : -68/77 : 1]

  [1 : 0 : 39/7 : -39/7 : -1/2 : 1/2 : 1]

  [1 : 0 : 0 : 0 : 149/170 : -149/170 : -32/85]

  [1 : -149/14 : -149/14 : 149/14 : 0 : 0 : -71/7]

  [1 : 173/190 : 173/190 : -173/190 : 78/95 : -78/95 : 17/95]

  [1 : 1 : 1 : -1 : 4/5 : -4/5 : 1/5]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 714 bases, 210 non-bases

  • circuits:

    • 4 circuits of size 4:

      {1, 2, 3, 4}, {0, 1, 4, 5}, {6, 7, 8, 11}, {8, 9, 10, 11}

    • 8 circuits of size 5:

      {0, 1, 2, 3, 5}, {0, 2, 3, 4, 5}, {0, 1, 2, 6, 7}, {2, 3, 7, 8, 9}, {3, 4, 5, 9, 10}, {6, 7, 8, 9, 10}, {0, 5, 6, 10, 11}, {6, 7, 9, 10, 11}

    • 48 circuits of size 6:

      {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 6, 7}, {0, 1, 3, 5, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 6, 7}, {1, 2, 4, 7, 8, 9}, {1, 3, 4, 7, 8, 9}, {0, 5, 6, 7, 8, 9}, {2, 3, 6, 7, 8, 10}, {0, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 9, 10}, {0, 1, 2, 4, 9, 10}, {0, 1, 3, 4, 9, 10}, {0, 2, 3, 4, 9, 10}, {0, 1, 2, 5, 9, 10}, {0, 1, 3, 5, 9, 10}, {0, 2, 3, 5, 9, 10}, {1, 2, 3, 5, 9, 10}, {0, 2, 4, 5, 9, 10}, {1, 2, 4, 5, 9, 10}, {2, 3, 6, 7, 9, 10}, {0, 5, 6, 7, 9, 10}, {2, 3, 6, 8, 9, 10}, {0, 5, 6, 8, 9, 10}, {0, 5, 7, 8, 9, 10}, {0, 1, 2, 6, 8, 11}, {0, 1, 2, 7, 8, 11}, {2, 3, 6, 7, 9, 11}, {0, 5, 6, 7, 9, 11}, {3, 4, 5, 8, 9, 11}, {2, 3, 6, 8, 9, 11}, {0, 5, 6, 8, 9, 11}, {0, 5, 7, 8, 9, 11}, {0, 1, 4, 6, 10, 11}, {1, 4, 5, 6, 10, 11}, {2, 3, 6, 7, 10, 11}, {3, 4, 5, 8, 10, 11}, {2, 3, 6, 8, 10, 11}, {2, 3, 7, 8, 10, 11}, {0, 5, 7, 8, 10, 11}, {2, 3, 6, 9, 10, 11}, {2, 3, 7, 9, 10, 11}, {0, 5, 7, 9, 10, 11}

    • 252 circuits of size 7:

      {0, 1, 2, 3, 6, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {0, 1, 2, 5, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 2, 5, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 2, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 6, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 3, 7, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {0, 1, 2, 5, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 6, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {0, 1, 2, 7, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {2, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 3, 7, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {3, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 3, 8, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 2, 3, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {2, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 3, 7, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 3, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {2, 3, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {3, 4, 5, 6, 7, 10, 11}, {0, 1, 2, 3, 8, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 4, 5, 6, 9, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 3, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {2, 4, 5, 7, 9, 10, 11}

---

---

46. Graph1246:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,6}, {0,6}, {5,7}, {1,8}, {2,10}, {3,9}, {4,11}

• Randomly generated (generic) hyperplane:

  48*a + 5*b + 12*c + 91*d + 54*e + 69*f + 11*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : -37/145 : -37/145 : 0 : -1]

  [0 : 1 : 0 : -1/29 : -1/29 : 0 : 0]

  [0 : 1 : 5/111 : 0 : -5/111 : -5/111 : 0]

  [0 : 1 : 1 : 106/91 : -1 : -1 : 0]

  [0 : 0 : 0 : 1 : -13/16 : -13/16 : 13/16]

  [1 : 0 : 0 : 1 : -5/8 : -13/8 : 5/8]

  [1 : 0 : 0 : 0 : 0 : 0 : -48/11]

  [1 : 0 : 0 : -24/11 : 0 : 24/11 : 0]

  [0 : 1 : 0 : 59/11 : -1 : -70/11 : 0]

  [0 : 1 : -118/79 : 118/79 : -1 : -1 : 0]

  [0 : 0 : 1 : -111/32 : 79/32 : 79/32 : 0]

  [0 : 0 : 0 : 1 : -1 : -1 : 32/11]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 756 bases, 168 non-bases

  • circuits:

    • 2 circuits of size 4:

      {0, 5, 6, 7}, {2, 3, 9, 10}

    • 16 circuits of size 5:

      {0, 1, 5, 6, 8}, {0, 1, 5, 7, 8}, {0, 1, 6, 7, 8}, {1, 5, 6, 7, 8}, {1, 2, 3, 8, 9}, {1, 2, 3, 8, 10}, {1, 2, 8, 9, 10}, {1, 3, 8, 9, 10}, {0, 4, 5, 6, 11}, {0, 4, 5, 7, 11}, {0, 4, 6, 7, 11}, {4, 5, 6, 7, 11}, {2, 3, 4, 9, 11}, {2, 3, 4, 10, 11}, {2, 4, 9, 10, 11}, {3, 4, 9, 10, 11}

    • 16 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {3, 4, 5, 7, 8, 9}, {1, 2, 3, 4, 8, 11}, {0, 1, 4, 5, 8, 11}, {0, 1, 4, 6, 8, 11}, {1, 4, 5, 6, 8, 11}, {0, 1, 4, 7, 8, 11}, {1, 4, 5, 7, 8, 11}, {1, 4, 6, 7, 8, 11}, {1, 2, 4, 8, 9, 11}, {1, 3, 4, 8, 9, 11}, {0, 1, 2, 6, 10, 11}, {1, 2, 4, 8, 10, 11}, {1, 3, 4, 8, 10, 11}, {1, 4, 8, 9, 10, 11}, {6, 7, 8, 9, 10, 11}

    • 376 circuits of size 7:

      {0, 1, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 4, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 1, 2, 3, 4, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 6, 9}, {0, 1, 2, 3, 5, 6, 9}, {0, 1, 2, 4, 5, 6, 9}, {0, 1, 3, 4, 5, 6, 9}, {0, 2, 3, 4, 5, 6, 9}, {1, 2, 3, 4, 5, 6, 9}, {0, 1, 2, 3, 4, 7, 9}, {0, 1, 2, 3, 5, 7, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 3, 6, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 1, 2, 4, 5, 6, 10}, {0, 1, 3, 4, 5, 6, 10}, {0, 2, 3, 4, 5, 6, 10}, {1, 2, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 4, 7, 10}, {0, 1, 2, 3, 5, 7, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 3, 6, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {2, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 2, 6, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {3, 4, 5, 6, 7, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {3, 4, 5, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {4, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {1, 2, 3, 4, 5, 6, 11}, {0, 1, 2, 3, 4, 7, 11}, {0, 1, 2, 3, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 3, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 3, 7, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {3, 4, 5, 6, 8, 9, 11}, {0, 1, 2, 7, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 3, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {0, 2, 6, 7, 8, 9, 11}, {1, 2, 6, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 3, 4, 5, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 3, 7, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {0, 3, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {3, 4, 5, 6, 8, 10, 11}, {0, 1, 2, 7, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {3, 4, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {3, 4, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {3, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {1, 4, 5, 6, 9, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {3, 5, 6, 7, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {0, 3, 5, 8, 9, 10, 11}, {0, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {3, 5, 6, 8, 9, 10, 11}, {4, 5, 6, 8, 9, 10, 11}, {0, 1, 7, 8, 9, 10, 11}, {0, 2, 7, 8, 9, 10, 11}, {0, 3, 7, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}, {3, 5, 7, 8, 9, 10, 11}, {4, 5, 7, 8, 9, 10, 11}

---

---

47. Graph1247:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {11,10}, {10,9}, {9,8}, {8,7}, {7,6}, {6,11}, {8,0}, {5,11}, {4,10}, {3,9}, {2,7}, {1,6}

• Randomly generated (generic) hyperplane:

  35*a + 22*b + 26*c + 33*d + 60*e + 13*f + 78*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 1 : 0 : -39/151 : 112/151 : -39/151]

  [0 : 0 : 1 : 0 : 0 : -2 : 0]

  [0 : 0 : 1 : -26/15 : -26/15 : 0 : 26/15]

  [0 : 1 : -2 : -2 : -1 : 0 : 2]

  [1 : -95/82 : 0 : 0 : -13/82 : 0 : 0]

  [1 : 0 : 0 : 0 : 56/151 : -95/151 : -95/151]

  [0 : 0 : 0 : 0 : 0 : 1 : -1/6]

  [0 : 0 : 0 : 1 : 1 : 0 : -31/26]

  [0 : 0 : 1 : 112/93 : 19/93 : 0 : -1]

  [0 : 1 : 22/19 : 22/19 : 0 : 0 : -22/19]

  [1 : -35/22 : 0 : 0 : 0 : 0 : 0]

  [1 : 0 : 0 : 0 : 0 : -5/13 : -5/13]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 750 bases, 174 non-bases

  • circuits:

    • 3 circuits of size 4:

      {1, 2, 6, 7}, {3, 4, 9, 10}, {4, 5, 10, 11}

    • 8 circuits of size 5:

      {0, 1, 2, 6, 8}, {0, 1, 2, 7, 8}, {0, 1, 6, 7, 8}, {0, 2, 6, 7, 8}, {2, 3, 7, 8, 9}, {0, 1, 5, 6, 11}, {3, 4, 5, 9, 11}, {3, 5, 9, 10, 11}

    • 41 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 6, 9}, {0, 1, 2, 3, 7, 9}, {0, 1, 3, 6, 7, 9}, {0, 2, 3, 6, 7, 9}, {0, 1, 2, 3, 8, 9}, {0, 3, 4, 5, 8, 9}, {0, 1, 3, 6, 8, 9}, {0, 2, 3, 6, 8, 9}, {1, 2, 3, 6, 8, 9}, {0, 1, 3, 7, 8, 9}, {0, 3, 6, 7, 8, 9}, {1, 3, 6, 7, 8, 9}, {0, 1, 4, 5, 6, 10}, {0, 3, 4, 5, 8, 10}, {2, 3, 4, 7, 8, 10}, {0, 3, 5, 8, 9, 10}, {0, 4, 5, 8, 9, 10}, {2, 4, 7, 8, 9, 10}, {0, 1, 2, 5, 7, 11}, {0, 2, 5, 6, 7, 11}, {0, 1, 2, 5, 8, 11}, {0, 3, 4, 5, 8, 11}, {0, 2, 5, 6, 8, 11}, {1, 2, 5, 6, 8, 11}, {0, 1, 5, 7, 8, 11}, {0, 2, 5, 7, 8, 11}, {1, 2, 5, 7, 8, 11}, {0, 5, 6, 7, 8, 11}, {1, 5, 6, 7, 8, 11}, {2, 5, 6, 7, 8, 11}, {0, 3, 4, 8, 9, 11}, {0, 3, 5, 8, 9, 11}, {0, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 10, 11}, {0, 3, 4, 8, 10, 11}, {0, 3, 5, 8, 10, 11}, {0, 3, 8, 9, 10, 11}, {0, 4, 8, 9, 10, 11}, {0, 5, 8, 9, 10, 11}, {6, 7, 8, 9, 10, 11}

    • 334 circuits of size 7:

      {0, 1, 3, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6, 7}, {0, 1, 3, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 4, 5, 6, 9}, {0, 1, 3, 4, 5, 6, 9}, {0, 2, 3, 4, 5, 6, 9}, {1, 2, 3, 4, 5, 6, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {0, 3, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 4, 5, 8, 9}, {1, 2, 3, 4, 5, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {0, 4, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 2, 3, 4, 5, 6, 10}, {1, 2, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 4, 7, 10}, {0, 1, 2, 3, 5, 7, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {0, 1, 3, 5, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {0, 3, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {2, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 4, 8, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {0, 4, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 4, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {0, 5, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {4, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 2, 3, 4, 5, 6, 11}, {1, 2, 3, 4, 5, 6, 11}, {0, 1, 2, 3, 4, 7, 11}, {0, 1, 3, 4, 5, 7, 11}, {0, 2, 3, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 3, 4, 6, 7, 11}, {0, 2, 3, 4, 6, 7, 11}, {0, 3, 4, 5, 6, 7, 11}, {1, 3, 4, 5, 6, 7, 11}, {2, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 4, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {3, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 4, 9, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 4, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {1, 2, 3, 4, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {4, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 4, 10, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 2, 3, 7, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {2, 3, 4, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {0, 1, 2, 3, 8, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {1, 2, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {0, 4, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {3, 4, 6, 7, 8, 10, 11}, {3, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 3, 9, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 2, 3, 7, 9, 10, 11}, {1, 2, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 3, 6, 7, 9, 10, 11}, {0, 4, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {0, 5, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {0, 1, 2, 8, 9, 10, 11}, {1, 2, 3, 8, 9, 10, 11}, {1, 2, 4, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 2, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {2, 3, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {0, 1, 7, 8, 9, 10, 11}, {0, 2, 7, 8, 9, 10, 11}, {1, 2, 7, 8, 9, 10, 11}, {1, 3, 7, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}

---

---

48. Graph1248:

• Edges of graph:

  {0,1}, {1,2}, {3,4}, {4,0}, {4,5}, {5,6}, {6,1}, {6,7}, {7,11}, {5,10}, {10,11}, {11,0}, {7,8}, {8,2}, {8,3}, {10,9}, {9,3}, {2,9}

• Randomly generated (generic) hyperplane:

  58*a + 44*b + 65*c + 36*d + 14*e + 14*f + 21*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 1 : -1 : 0 : 0 : 0 : 1]

  [0 : 0 : 1 : 0 : -22/7 : 0 : -1]

  [1 : 0 : 0 : -1 : -18/7 : 1 : 0]

  [0 : 1 : 1 : 137/13 : -124/13 : -124/13 : -137/13]

  [0 : 1 : -44/93 : 0 : -44/93 : -44/93 : 0]

  [1 : 0 : -23/93 : 0 : -23/93 : -116/93 : -1]

  [1 : 0 : -1 : 0 : -1 : 0 : 1]

  [1 : -29/51 : -29/51 : 0 : 0 : -29/51 : 29/51]

  [1 : -9/31 : -9/31 : -40/31 : 0 : 1 : 9/31]

  [1 : 0 : 0 : 37/13 : -37/13 : -37/13 : -50/13]

  [1 : 0 : 0 : 0 : 0 : -37/14 : -1]

  [0 : 1 : 1 : 0 : 0 : -44/7 : -1]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 816 bases, 108 non-bases

  • circuits:

    • 1 circuit of size 4:

      {2, 3, 8, 9}

    • 6 circuits of size 5:

      {0, 1, 4, 5, 6}, {1, 2, 6, 7, 8}, {3, 4, 5, 9, 10}, {0, 1, 6, 7, 11}, {0, 4, 5, 10, 11}, {5, 6, 7, 10, 11}

    • 38 circuits of size 6:

      {0, 1, 2, 3, 4, 8}, {3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 9}, {1, 2, 3, 6, 7, 9}, {0, 1, 2, 4, 8, 9}, {0, 1, 3, 4, 8, 9}, {1, 3, 6, 7, 8, 9}, {0, 1, 4, 5, 7, 10}, {0, 1, 4, 6, 7, 10}, {0, 1, 5, 6, 7, 10}, {0, 4, 5, 6, 7, 10}, {1, 4, 5, 6, 7, 10}, {2, 3, 4, 5, 8, 10}, {1, 2, 5, 6, 9, 10}, {2, 4, 5, 8, 9, 10}, {0, 1, 4, 5, 7, 11}, {0, 4, 5, 6, 7, 11}, {1, 4, 5, 6, 7, 11}, {0, 1, 2, 6, 8, 11}, {0, 1, 2, 7, 8, 11}, {0, 3, 4, 7, 8, 11}, {0, 2, 6, 7, 8, 11}, {0, 3, 4, 5, 9, 11}, {0, 1, 4, 6, 10, 11}, {0, 1, 5, 6, 10, 11}, {1, 4, 5, 6, 10, 11}, {0, 1, 4, 7, 10, 11}, {0, 1, 5, 7, 10, 11}, {1, 4, 5, 7, 10, 11}, {0, 4, 6, 7, 10, 11}, {1, 4, 6, 7, 10, 11}, {2, 3, 7, 8, 10, 11}, {0, 1, 2, 9, 10, 11}, {0, 3, 4, 9, 10, 11}, {0, 3, 5, 9, 10, 11}, {2, 3, 7, 9, 10, 11}, {2, 7, 8, 9, 10, 11}, {3, 7, 8, 9, 10, 11}

    • 440 circuits of size 7:

      {0, 1, 2, 3, 4, 5, 7}, {0, 1, 2, 3, 4, 6, 7}, {0, 1, 2, 3, 5, 6, 7}, {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 5, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 1, 2, 3, 5, 7, 8}, {0, 1, 2, 4, 5, 7, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 3, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {0, 1, 3, 5, 6, 7, 8}, {0, 2, 3, 5, 6, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 5, 6, 9}, {0, 2, 3, 4, 5, 6, 9}, {1, 2, 3, 4, 5, 6, 9}, {0, 1, 2, 3, 5, 7, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {0, 1, 2, 5, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 3, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 5, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {0, 1, 2, 5, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {0, 1, 5, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {0, 4, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 5, 10}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 2, 3, 4, 5, 6, 10}, {1, 2, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 4, 7, 10}, {0, 1, 2, 3, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 3, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {2, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 1, 2, 3, 6, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 3, 7, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 2, 5, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 2, 3, 6, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {0, 1, 2, 3, 7, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 1, 2, 6, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 1, 2, 6, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {0, 1, 2, 7, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {0, 1, 6, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {0, 5, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {4, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 5, 11}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 2, 3, 4, 5, 6, 11}, {1, 2, 3, 4, 5, 6, 11}, {0, 1, 2, 3, 4, 7, 11}, {0, 1, 2, 3, 5, 7, 11}, {0, 2, 3, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {2, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {1, 2, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {2, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 3, 7, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {3, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 4, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {3, 4, 5, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {0, 4, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {3, 4, 5, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {0, 5, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {4, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 4, 10, 11}, {0, 1, 2, 3, 5, 10, 11}, {1, 2, 3, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {2, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 3, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {1, 2, 3, 4, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {2, 3, 4, 5, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {2, 3, 4, 6, 7, 10, 11}, {0, 1, 2, 3, 8, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {3, 4, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {3, 4, 5, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {3, 4, 6, 7, 8, 10, 11}, {1, 2, 3, 4, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {2, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {2, 4, 5, 6, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 4, 5, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {3, 4, 6, 7, 9, 10, 11}, {0, 1, 3, 8, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {1, 2, 4, 8, 9, 10, 11}, {1, 3, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {3, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {3, 5, 6, 8, 9, 10, 11}, {4, 5, 6, 8, 9, 10, 11}, {0, 1, 7, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {4, 5, 7, 8, 9, 10, 11}, {0, 6, 7, 8, 9, 10, 11}, {1, 6, 7, 8, 9, 10, 11}, {4, 6, 7, 8, 9, 10, 11}

---

---

49. Graph1249:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {4,5}, {5,6}, {6,3}, {6,7}, {7,8}, {8,2}, {8,9}, {9,10}, {10,1}, {10,11}, {11,0}, {7,11}, {5,9}

• Randomly generated (generic) hyperplane:

  99*a + 58*b + 37*c + 54*d + 83*e + 86*f + 52*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 0 : 1 : 0 : -83/52]

  [0 : 0 : 0 : 1 : -2/135 : 0 : -137/135]

  [0 : 1 : 0 : -144/137 : -144/137 : 1 : 0]

  [1 : -91/72 : 0 : 0 : 1 : -91/72 : 0]

  [1 : 0 : 0 : 0 : -99/83 : 0 : 0]

  [1 : -33/8 : 33/8 : 0 : 33/8 : -33/8 : 0]

  [1 : -1 : -38/37 : 0 : 1 : -1 : 0]

  [0 : 0 : 1 : 0 : -37/49 : 37/49 : -37/49]

  [0 : 1 : 7/12 : -1 : -19/12 : 19/12 : -7/12]

  [0 : 1 : -1 : -24/5 : 19/5 : -19/5 : 24/5]

  [0 : 0 : 0 : 1 : 2/3 : -2/3 : -1]

  [0 : 0 : 0 : 0 : 1 : -1 : 3/52]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 786 bases, 138 non-bases

  • circuits:

    • 2 circuits of size 4:

      {3, 4, 5, 6}, {0, 1, 10, 11}

    • 5 circuits of size 5:

      {0, 1, 2, 3, 4}, {2, 3, 6, 7, 8}, {5, 6, 7, 8, 9}, {1, 2, 8, 9, 10}, {7, 8, 9, 10, 11}

    • 47 circuits of size 6:

      {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 6}, {2, 3, 4, 5, 7, 8}, {2, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 7, 9}, {2, 3, 4, 6, 7, 9}, {2, 3, 5, 6, 7, 9}, {2, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 8, 9}, {2, 3, 4, 6, 8, 9}, {2, 3, 5, 6, 8, 9}, {2, 4, 5, 6, 8, 9}, {0, 1, 2, 7, 8, 9}, {2, 3, 4, 7, 8, 9}, {2, 3, 5, 7, 8, 9}, {2, 4, 5, 7, 8, 9}, {3, 4, 5, 7, 8, 9}, {2, 4, 6, 7, 8, 9}, {3, 4, 6, 7, 8, 9}, {0, 1, 2, 7, 8, 10}, {0, 1, 4, 5, 9, 10}, {0, 1, 2, 7, 9, 10}, {0, 1, 7, 8, 9, 10}, {0, 2, 7, 8, 9, 10}, {0, 3, 4, 5, 7, 11}, {0, 3, 4, 6, 7, 11}, {0, 3, 5, 6, 7, 11}, {0, 4, 5, 6, 7, 11}, {0, 1, 2, 7, 8, 11}, {0, 1, 4, 5, 9, 11}, {0, 1, 2, 7, 9, 11}, {0, 1, 2, 8, 9, 11}, {0, 1, 7, 8, 9, 11}, {0, 2, 7, 8, 9, 11}, {1, 2, 7, 8, 9, 11}, {0, 2, 3, 4, 10, 11}, {1, 2, 3, 4, 10, 11}, {0, 2, 7, 8, 10, 11}, {1, 2, 7, 8, 10, 11}, {5, 6, 7, 8, 10, 11}, {0, 4, 5, 9, 10, 11}, {1, 4, 5, 9, 10, 11}, {0, 2, 7, 9, 10, 11}, {1, 2, 7, 9, 10, 11}, {5, 6, 7, 9, 10, 11}, {0, 2, 8, 9, 10, 11}, {5, 6, 8, 9, 10, 11}

    • 379 circuits of size 7:

      {0, 1, 2, 3, 5, 7, 8}, {0, 1, 2, 4, 5, 7, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 1, 2, 4, 6, 7, 8}, {0, 1, 3, 4, 6, 7, 8}, {0, 1, 2, 5, 6, 7, 8}, {0, 1, 3, 5, 6, 7, 8}, {0, 1, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 5, 7, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 1, 2, 3, 6, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 1, 2, 5, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 1, 2, 3, 5, 8, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 1, 2, 3, 6, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 1, 2, 5, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 1, 2, 3, 5, 7, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 3, 6, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 1, 2, 5, 6, 7, 10}, {0, 1, 3, 5, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {0, 1, 4, 5, 6, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 3, 6, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {0, 1, 5, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {0, 4, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 2, 3, 4, 5, 9, 10}, {1, 2, 3, 4, 5, 9, 10}, {0, 1, 2, 3, 6, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {0, 4, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 2, 3, 4, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {1, 3, 6, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 5, 7, 11}, {0, 1, 2, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {0, 1, 2, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 1, 2, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 1, 4, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {0, 1, 5, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 2, 3, 4, 5, 9, 11}, {1, 2, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 2, 3, 4, 8, 9, 11}, {1, 2, 3, 4, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 4, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {0, 4, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {2, 3, 4, 5, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {2, 3, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 3, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {2, 3, 4, 5, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 4, 5, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {2, 3, 4, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {0, 4, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {3, 4, 5, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {0, 4, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {3, 4, 6, 7, 8, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {2, 3, 4, 5, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {2, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {2, 4, 5, 6, 9, 10, 11}, {0, 3, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {2, 3, 4, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}, {2, 4, 5, 7, 9, 10, 11}, {3, 4, 5, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 3, 6, 7, 9, 10, 11}, {0, 4, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {3, 4, 6, 7, 9, 10, 11}, {0, 3, 4, 8, 9, 10, 11}, {1, 3, 4, 8, 9, 10, 11}, {2, 3, 4, 8, 9, 10, 11}, {0, 3, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {2, 3, 5, 8, 9, 10, 11}, {2, 4, 5, 8, 9, 10, 11}, {3, 4, 5, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {2, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {3, 4, 6, 8, 9, 10, 11}

---

---

50. Graph1250:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {0,5}, {5,6}, {6,7}, {7,2}, {1,8}, {8,6}, {4,11}, {11,10}, {10,9}, {9,3}, {5,9}, {8,10}, {7,11}

• Randomly generated (generic) hyperplane:

  17*a + 24*b + 68*c + 60*d + 26*e + 70*f + 46*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 1 : -30/13 : 0 : 0]

  [0 : 0 : 0 : 1 : -1 : 0 : -17/23]

  [0 : 1 : 0 : 0 : 0 : 0 : -12/23]

  [0 : 1 : 12/67 : -12/67 : -12/67 : -12/67 : -12/67]

  [0 : 0 : 1 : -1 : 54/13 : -1 : -1]

  [1 : 0 : 0 : -17/60 : 0 : 0 : 0]

  [1 : -17/46 : -17/46 : 0 : 0 : 0 : 17/46]

  [0 : 1 : 11/34 : 0 : 0 : 0 : -1]

  [1 : -1 : -1 : 29/80 : -29/80 : 0 : 109/80]

  [1 : -43/110 : -43/110 : -67/110 : 43/110 : 43/110 : 43/110]

  [1 : -1 : -1 : -67/176 : 1 : 109/176 : 109/176]

  [0 : 0 : 1 : -17/44 : 0 : -17/44 : -17/44]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 840 bases, 84 non-bases

  • circuits:

    • 8 circuits of size 5:

      {0, 1, 2, 3, 4}, {0, 1, 5, 6, 8}, {1, 2, 6, 7, 8}, {0, 3, 4, 5, 9}, {5, 6, 8, 9, 10}, {2, 3, 4, 7, 11}, {6, 7, 8, 10, 11}, {3, 4, 9, 10, 11}

    • 28 circuits of size 6:

      {0, 1, 2, 5, 6, 7}, {0, 1, 2, 5, 7, 8}, {0, 2, 5, 6, 7, 8}, {0, 1, 2, 3, 5, 9}, {0, 1, 2, 4, 5, 9}, {1, 2, 3, 4, 5, 9}, {2, 3, 5, 6, 7, 9}, {0, 1, 5, 6, 9, 10}, {2, 3, 4, 7, 9, 10}, {1, 2, 3, 8, 9, 10}, {0, 1, 5, 8, 9, 10}, {0, 1, 6, 8, 9, 10}, {0, 1, 2, 3, 7, 11}, {0, 1, 2, 4, 7, 11}, {0, 1, 3, 4, 7, 11}, {0, 4, 5, 6, 7, 11}, {5, 6, 7, 8, 9, 11}, {0, 3, 4, 5, 10, 11}, {1, 2, 6, 7, 10, 11}, {0, 1, 4, 8, 10, 11}, {1, 2, 6, 8, 10, 11}, {1, 2, 7, 8, 10, 11}, {0, 3, 5, 9, 10, 11}, {0, 4, 5, 9, 10, 11}, {2, 3, 7, 9, 10, 11}, {2, 4, 7, 9, 10, 11}, {5, 6, 7, 9, 10, 11}, {5, 7, 8, 9, 10, 11}

    • 488 circuits of size 7:

      {0, 1, 3, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 3, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 6, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 3, 6, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 4, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 2, 3, 7, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {1, 2, 3, 4, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {0, 4, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 5, 6, 10}, {0, 1, 2, 4, 5, 6, 10}, {0, 1, 3, 4, 5, 6, 10}, {0, 2, 3, 4, 5, 6, 10}, {1, 2, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 5, 7, 10}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 2, 3, 6, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 1, 3, 5, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {0, 1, 4, 5, 6, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {0, 3, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {2, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 3, 6, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 3, 7, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {0, 4, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 6, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {2, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 3, 7, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 2, 6, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {0, 4, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {3, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 2, 3, 4, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {2, 3, 4, 5, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {0, 1, 2, 7, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {1, 3, 6, 7, 8, 9, 10}, {2, 3, 6, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 5, 6, 11}, {0, 1, 2, 4, 5, 6, 11}, {0, 1, 3, 4, 5, 6, 11}, {0, 2, 3, 4, 5, 6, 11}, {1, 2, 3, 4, 5, 6, 11}, {0, 1, 3, 5, 6, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {1, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {3, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {2, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {3, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 3, 8, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 2, 3, 4, 8, 9, 11}, {1, 2, 3, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {2, 3, 4, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {0, 4, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {3, 4, 5, 6, 8, 9, 11}, {0, 1, 2, 7, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 3, 7, 8, 9, 11}, {1, 2, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {0, 4, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {3, 4, 5, 7, 8, 9, 11}, {0, 1, 6, 7, 8, 9, 11}, {0, 2, 6, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {1, 2, 3, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 4, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {2, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {0, 1, 5, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {3, 4, 5, 6, 7, 10, 11}, {0, 1, 2, 3, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {2, 3, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 4, 5, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {3, 4, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {0, 4, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {3, 4, 5, 7, 8, 10, 11}, {0, 1, 2, 3, 9, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {1, 4, 5, 6, 9, 10, 11}, {2, 4, 5, 6, 9, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {0, 4, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {0, 1, 2, 8, 9, 10, 11}, {0, 1, 3, 8, 9, 10, 11}, {0, 2, 3, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {1, 2, 4, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {2, 3, 5, 8, 9, 10, 11}, {1, 4, 5, 8, 9, 10, 11}, {2, 4, 5, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {2, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {0, 1, 7, 8, 9, 10, 11}, {0, 2, 7, 8, 9, 10, 11}, {0, 3, 7, 8, 9, 10, 11}, {1, 3, 7, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}

---

---

51. Graph1251:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,0}, {8,9}, {9,10}, {10,11}, {11,8}, {0,9}, {2,10}, {4,11}, {6,8}, {3,7}, {1,5}

• Randomly generated (generic) hyperplane:

  11*a + 92*b + 98*c + 68*d + 94*e + 31*f + 8*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 113/92 : -1 : 1 : -1 : 0 : 0]

  [0 : 1 : -92/129 : 0 : 0 : -92/129 : 0]

  [0 : 1 : 1 : -221/29 : 0 : 250/29 : 221/29]

  [0 : 1 : -76/49 : 1 : 0 : 0 : -1]

  [0 : 0 : 1 : 0 : -49/47 : 0 : 0]

  [0 : 0 : 1 : 0 : -43/21 : 64/21 : 0]

  [1 : -1 : -1 : 0 : 202/63 : -265/63 : 1]

  [1 : 113/152 : -1 : 265/152 : -1 : 0 : -113/152]

  [1 : -1 : -1 : 0 : 218/55 : -273/55 : -273/55]

  [1 : -1 : -1 : 273/68 : -1 : 0 : 0]

  [0 : 0 : 0 : 1 : 0 : -68/39 : -68/39]

  [0 : 0 : 0 : 0 : 1 : -94/39 : -94/39]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 804 bases, 120 non-bases

  • circuits:

    • 1 circuit of size 4:

      {8, 9, 10, 11}

    • 8 circuits of size 5:

      {1, 2, 3, 4, 5}, {0, 1, 2, 3, 7}, {0, 1, 5, 6, 7}, {3, 4, 5, 6, 7}, {0, 6, 7, 8, 9}, {0, 1, 2, 9, 10}, {4, 5, 6, 8, 11}, {2, 3, 4, 10, 11}

    • 36 circuits of size 6:

      {0, 1, 2, 3, 4, 6}, {0, 1, 2, 3, 5, 6}, {0, 1, 2, 4, 5, 6}, {0, 1, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 7}, {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 2, 3, 4, 6, 7}, {1, 2, 3, 4, 6, 7}, {0, 2, 3, 5, 6, 7}, {1, 2, 3, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {0, 1, 5, 6, 8, 9}, {0, 1, 5, 7, 8, 9}, {1, 5, 6, 7, 8, 9}, {0, 1, 3, 7, 9, 10}, {0, 2, 3, 7, 9, 10}, {1, 2, 3, 7, 9, 10}, {2, 3, 4, 8, 9, 10}, {4, 5, 6, 8, 9, 10}, {3, 4, 5, 7, 8, 11}, {3, 4, 6, 7, 8, 11}, {3, 5, 6, 7, 8, 11}, {0, 1, 2, 8, 9, 11}, {2, 3, 4, 8, 9, 11}, {1, 2, 3, 5, 10, 11}, {1, 2, 4, 5, 10, 11}, {1, 3, 4, 5, 10, 11}, {0, 1, 2, 8, 10, 11}, {0, 6, 7, 8, 10, 11}, {4, 5, 6, 9, 10, 11}, {0, 6, 7, 9, 10, 11}

    • 416 circuits of size 7:

      {0, 1, 2, 3, 4, 8, 9}, {0, 1, 2, 3, 5, 8, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {0, 1, 2, 3, 6, 8, 9}, {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 4, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 3, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {1, 2, 3, 4, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {1, 2, 3, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 8, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 3, 6, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 2, 5, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 1, 2, 6, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {1, 2, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {0, 4, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 2, 3, 4, 5, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {2, 3, 4, 5, 6, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {2, 3, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 4, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {1, 2, 6, 7, 8, 9, 10}, {1, 3, 6, 7, 8, 9, 10}, {2, 3, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 8, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 2, 5, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 1, 2, 6, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 4, 9, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 2, 3, 4, 5, 9, 11}, {0, 1, 2, 3, 6, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {2, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 1, 2, 6, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 4, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 3, 7, 8, 9, 11}, {1, 2, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {0, 4, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {1, 2, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 1, 2, 5, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {0, 1, 4, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {0, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {0, 3, 4, 5, 7, 10, 11}, {0, 1, 2, 6, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {0, 4, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {0, 3, 4, 5, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {1, 2, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {0, 4, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {2, 4, 5, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {1, 5, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {0, 1, 4, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {0, 3, 4, 5, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 3, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}, {0, 4, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {2, 4, 5, 7, 9, 10, 11}, {3, 4, 5, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 3, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {3, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {3, 5, 6, 7, 9, 10, 11}

---

---

52. Graph1252:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {0,6}, {6,7}, {7,2}, {8,9}, {3,11}, {11,10}, {10,5}, {4,8}, {8,6}, {1,9}, {9,11}, {7,10}

• Randomly generated (generic) hyperplane:

  78*a + 57*b + 89*c + 6*d + 55*e + 87*f + 44*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : -23/13 : 0 : 0 : -1 : 0 : 23/13]

  [0 : 1 : -13/89 : 0 : 0 : 0 : -1]

  [0 : 0 : 1 : -89/17 : -89/17 : 0 : 89/17]

  [0 : 0 : 1 : -50/3 : 1 : 0 : -1]

  [1 : -1 : 0 : 11 : 0 : -1 : 0]

  [1 : -1 : 0 : 1/7 : -6/7 : -1/7 : 6/7]

  [1 : 0 : 0 : 0 : -9/32 : -23/32 : 0]

  [0 : 0 : 0 : 1 : 49/32 : -17/32 : -1]

  [1 : 3/19 : 0 : 0 : 0 : -1 : 0]

  [0 : 1 : -19/15 : 0 : 0 : 0 : 19/15]

  [0 : 0 : 0 : 1 : 25/11 : -1 : -1]

  [0 : 0 : 1 : 0 : -9/11 : 0 : -1]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 840 bases, 84 non-bases

  • circuits:

    • 8 circuits of size 5:

      {0, 1, 2, 6, 7}, {0, 4, 5, 6, 8}, {0, 1, 6, 8, 9}, {0, 5, 6, 7, 10}, {1, 2, 3, 9, 11}, {3, 4, 8, 9, 11}, {3, 4, 5, 10, 11}, {2, 3, 7, 10, 11}

    • 28 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {2, 3, 4, 6, 7, 8}, {0, 1, 4, 5, 6, 9}, {1, 2, 3, 4, 8, 9}, {0, 1, 4, 5, 8, 9}, {1, 4, 5, 6, 8, 9}, {0, 1, 2, 7, 8, 9}, {0, 2, 6, 7, 8, 9}, {1, 2, 6, 7, 8, 9}, {0, 1, 2, 5, 6, 10}, {0, 1, 2, 5, 7, 10}, {2, 3, 4, 5, 7, 10}, {1, 2, 5, 6, 7, 10}, {0, 4, 5, 7, 8, 10}, {0, 4, 6, 7, 8, 10}, {4, 5, 6, 7, 8, 10}, {1, 2, 3, 7, 9, 10}, {3, 4, 5, 8, 9, 10}, {2, 3, 4, 5, 7, 11}, {1, 2, 3, 4, 8, 11}, {1, 2, 4, 8, 9, 11}, {2, 4, 5, 7, 10, 11}, {0, 1, 5, 9, 10, 11}, {1, 2, 7, 9, 10, 11}, {1, 3, 7, 9, 10, 11}, {3, 5, 8, 9, 10, 11}, {4, 5, 8, 9, 10, 11}, {6, 7, 8, 9, 10, 11}

    • 488 circuits of size 7:

      {0, 1, 3, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 4, 6, 8}, {0, 1, 2, 3, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 1, 2, 3, 4, 7, 8}, {0, 1, 2, 3, 5, 7, 8}, {0, 1, 2, 4, 5, 7, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 3, 4, 6, 7, 8}, {0, 1, 3, 5, 6, 7, 8}, {0, 2, 3, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 4, 6, 9}, {0, 1, 2, 3, 5, 6, 9}, {0, 2, 3, 4, 5, 6, 9}, {1, 2, 3, 4, 5, 6, 9}, {0, 1, 2, 3, 4, 7, 9}, {0, 1, 2, 3, 5, 7, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 3, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 3, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {1, 2, 3, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 3, 4, 5, 6, 10}, {0, 2, 3, 4, 5, 6, 10}, {1, 2, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 4, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 4, 8, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 3, 6, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 3, 7, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {1, 2, 3, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 4, 9, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 2, 3, 4, 5, 9, 10}, {1, 2, 3, 4, 5, 9, 10}, {0, 1, 2, 3, 6, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {2, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {3, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 3, 8, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 2, 3, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {2, 4, 5, 6, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {2, 3, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {1, 3, 6, 7, 8, 9, 10}, {2, 3, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 1, 2, 4, 5, 6, 11}, {0, 1, 3, 4, 5, 6, 11}, {0, 2, 3, 4, 5, 6, 11}, {1, 2, 3, 4, 5, 6, 11}, {0, 1, 2, 3, 4, 7, 11}, {0, 1, 2, 3, 5, 7, 11}, {0, 1, 2, 4, 5, 7, 11}, {0, 1, 3, 4, 5, 7, 11}, {0, 1, 3, 4, 6, 7, 11}, {0, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 1, 3, 5, 6, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {0, 1, 4, 5, 6, 7, 11}, {0, 2, 4, 5, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {0, 3, 4, 5, 6, 7, 11}, {1, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 3, 7, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {0, 1, 2, 5, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {0, 1, 3, 6, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {0, 1, 5, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {3, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 2, 3, 4, 5, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {2, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 1, 3, 6, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 4, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {3, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {2, 4, 5, 6, 8, 9, 11}, {0, 1, 3, 7, 8, 9, 11}, {0, 2, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {0, 4, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {2, 4, 5, 7, 8, 9, 11}, {0, 3, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {0, 5, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {4, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 4, 10, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 1, 2, 4, 6, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 4, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 1, 3, 6, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {0, 1, 2, 3, 8, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {1, 4, 5, 6, 8, 10, 11}, {2, 4, 5, 6, 8, 10, 11}, {0, 1, 2, 7, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {1, 4, 5, 7, 8, 10, 11}, {0, 1, 6, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {1, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {3, 4, 6, 7, 8, 10, 11}, {1, 5, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {3, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 2, 3, 4, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {0, 2, 4, 5, 9, 10, 11}, {1, 2, 4, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {0, 1, 4, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {2, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {0, 4, 5, 6, 9, 10, 11}, {1, 4, 5, 6, 9, 10, 11}, {2, 4, 5, 6, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {0, 3, 4, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {0, 4, 5, 7, 9, 10, 11}, {1, 4, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {0, 4, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {3, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {3, 5, 6, 7, 9, 10, 11}, {4, 5, 6, 7, 9, 10, 11}, {0, 1, 2, 8, 9, 10, 11}, {0, 1, 3, 8, 9, 10, 11}, {0, 2, 3, 8, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 2, 4, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {2, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {2, 4, 6, 8, 9, 10, 11}, {0, 5, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {2, 5, 6, 8, 9, 10, 11}, {0, 1, 7, 8, 9, 10, 11}, {0, 2, 7, 8, 9, 10, 11}, {0, 3, 7, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {2, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}, {2, 5, 7, 8, 9, 10, 11}

---

---

53. Graph1253:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,0}, {2,4}, {4,5}, {5,6}, {6,1}, {4,9}, {5,8}, {6,7}, {7,8}, {8,9}, {9,10}, {10,11}, {11,7}, {10,0}, {3,11}

• Randomly generated (generic) hyperplane:

  18*a + 41*b + 31*c + 80*d + 83*e + 13*f + 76*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 0 : 1 : 0 : -83/76]

  [0 : 0 : 1 : -1 : 0 : -1 : 31/38]

  [0 : 1 : -21/31 : 21/31 : -1 : 21/31 : 0]

  [0 : 1 : 1 : -1 : 21/83 : -1 : 0]

  [0 : 1 : 42/31 : 0 : -1 : 0 : 0]

  [1 : 0 : 64/31 : 0 : 1 : -1 : -2]

  [1 : 0 : 35/46 : 11/46 : 1 : -35/46 : -81/46]

  [1 : 0 : 0 : 1 : 1 : -105/89 : -194/89]

  [1 : 0 : 0 : 4/5 : 1 : -1 : -2]

  [0 : 1 : 1 : 11/80 : -1 : 0 : 0]

  [0 : 1 : 1 : -1 : 12 : 0 : -13]

  [0 : 1 : 1 : -1 : -2 : 98/89 : 187/89]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 726 bases, 198 non-bases

  • circuits:

    • 4 circuits of size 4:

      {0, 1, 2, 3}, {5, 6, 7, 8}, {4, 5, 8, 9}, {0, 3, 10, 11}

    • 6 circuits of size 5:

      {1, 2, 4, 5, 6}, {4, 5, 6, 7, 9}, {4, 6, 7, 8, 9}, {0, 1, 2, 10, 11}, {1, 2, 3, 10, 11}, {7, 8, 9, 10, 11}

    • 50 circuits of size 6:

      {0, 1, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 6}, {1, 2, 4, 5, 7, 8}, {1, 2, 4, 6, 7, 8}, {1, 2, 4, 5, 7, 9}, {1, 2, 4, 6, 7, 9}, {1, 2, 5, 6, 7, 9}, {1, 2, 4, 6, 8, 9}, {1, 2, 5, 6, 8, 9}, {1, 2, 4, 7, 8, 9}, {1, 2, 5, 7, 8, 9}, {1, 2, 6, 7, 8, 9}, {0, 1, 2, 6, 7, 10}, {0, 1, 3, 6, 7, 10}, {0, 2, 3, 6, 7, 10}, {1, 2, 3, 6, 7, 10}, {0, 1, 2, 4, 9, 10}, {0, 1, 3, 4, 9, 10}, {0, 2, 3, 4, 9, 10}, {1, 2, 3, 4, 9, 10}, {0, 3, 7, 8, 9, 10}, {0, 1, 2, 6, 7, 11}, {0, 1, 3, 6, 7, 11}, {0, 2, 3, 6, 7, 11}, {1, 2, 3, 6, 7, 11}, {0, 1, 2, 4, 9, 11}, {0, 1, 3, 4, 9, 11}, {0, 2, 3, 4, 9, 11}, {1, 2, 3, 4, 9, 11}, {0, 3, 7, 8, 9, 11}, {0, 1, 6, 7, 10, 11}, {0, 2, 6, 7, 10, 11}, {1, 2, 6, 7, 10, 11}, {1, 3, 6, 7, 10, 11}, {2, 3, 6, 7, 10, 11}, {4, 5, 6, 7, 10, 11}, {4, 5, 6, 8, 10, 11}, {4, 5, 7, 8, 10, 11}, {4, 6, 7, 8, 10, 11}, {0, 1, 4, 9, 10, 11}, {0, 2, 4, 9, 10, 11}, {1, 2, 4, 9, 10, 11}, {1, 3, 4, 9, 10, 11}, {2, 3, 4, 9, 10, 11}, {4, 5, 6, 9, 10, 11}, {4, 5, 7, 9, 10, 11}, {4, 6, 7, 9, 10, 11}, {5, 6, 7, 9, 10, 11}, {4, 6, 8, 9, 10, 11}, {5, 6, 8, 9, 10, 11}

    • 282 circuits of size 7:

      {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {0, 1, 3, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {0, 1, 3, 6, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {0, 1, 2, 4, 5, 7, 10}, {0, 1, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {1, 2, 3, 4, 5, 7, 10}, {0, 1, 4, 5, 6, 7, 10}, {0, 2, 4, 5, 6, 7, 10}, {0, 3, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {2, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 2, 5, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {2, 3, 4, 5, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {2, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {2, 3, 4, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 2, 6, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {0, 1, 2, 7, 8, 9, 10}, {1, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {2, 3, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {2, 3, 5, 7, 8, 9, 10}, {0, 1, 6, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {1, 3, 6, 7, 8, 9, 10}, {2, 3, 6, 7, 8, 9, 10}, {0, 1, 2, 4, 5, 7, 11}, {0, 1, 3, 4, 5, 7, 11}, {0, 2, 3, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 4, 5, 6, 7, 11}, {0, 2, 4, 5, 6, 7, 11}, {0, 3, 4, 5, 6, 7, 11}, {1, 3, 4, 5, 6, 7, 11}, {2, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 1, 4, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 2, 5, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 1, 4, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {2, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {2, 3, 4, 5, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {0, 1, 2, 6, 8, 9, 11}, {0, 1, 3, 6, 8, 9, 11}, {0, 2, 3, 6, 8, 9, 11}, {1, 2, 3, 6, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {2, 3, 4, 6, 8, 9, 11}, {0, 1, 5, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {0, 1, 2, 7, 8, 9, 11}, {1, 2, 3, 7, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {2, 3, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {2, 3, 5, 7, 8, 9, 11}, {0, 1, 6, 7, 8, 9, 11}, {0, 2, 6, 7, 8, 9, 11}, {1, 3, 6, 7, 8, 9, 11}, {2, 3, 6, 7, 8, 9, 11}, {0, 1, 4, 5, 6, 10, 11}, {0, 2, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {2, 3, 4, 5, 6, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {1, 3, 4, 5, 7, 10, 11}, {2, 3, 4, 5, 7, 10, 11}, {0, 1, 4, 5, 8, 10, 11}, {0, 2, 4, 5, 8, 10, 11}, {1, 2, 4, 5, 8, 10, 11}, {1, 3, 4, 5, 8, 10, 11}, {2, 3, 4, 5, 8, 10, 11}, {0, 1, 4, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 1, 5, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {2, 3, 4, 7, 8, 10, 11}, {0, 1, 5, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {0, 1, 5, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 2, 5, 8, 9, 10, 11}, {1, 2, 5, 8, 9, 10, 11}, {1, 3, 5, 8, 9, 10, 11}, {2, 3, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 2, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {2, 3, 6, 8, 9, 10, 11}

---

---

54. Graph1254:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {0,6}, {2,6}, {6,11}, {1,7}, {3,7}, {7,8}, {8,10}, {10,9}, {4,9}, {9,11}, {11,8}, {5,10}

• Randomly generated (generic) hyperplane:

  85*a + 50*b + 85*c + 48*d + 77*e + 17*f + g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 1 : -85/24 : 0 : 0 : 0]

  [1 : 0 : 1 : -187/48 : 0 : 1 : 0]

  [1 : 0 : 179/40 : -179/40 : -139/40 : 1 : 0]

  [0 : 0 : 1 : -103/143 : -103/143 : 40/143 : 40/143]

  [0 : 1 : 1 : -135/143 : -135/143 : -135/143 : -135/143]

  [1 : -34/27 : -7/27 : 0 : 0 : 0 : 0]

  [1 : 0 : 179/57 : -179/57 : -122/57 : -122/57 : 0]

  [1 : 0 : -84/103 : 0 : 0 : -84/103 : -187/103]

  [1 : 0 : 0 : 0 : 0 : 0 : -85]

  [0 : 1 : 25/29 : -25/29 : -25/29 : -25/29 : -25/29]

  [1 : -17/10 : 0 : 0 : 0 : 0 : 0]

  [0 : 0 : 1 : -1 : -1 : -1 : 57]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 736 bases, 188 non-bases

  • circuits:

    • 4 circuits of size 4:

      {0, 1, 2, 6}, {1, 2, 3, 7}, {4, 5, 9, 10}, {8, 9, 10, 11}

    • 4 circuits of size 5:

      {0, 1, 3, 6, 7}, {0, 2, 3, 6, 7}, {4, 5, 8, 9, 11}, {4, 5, 8, 10, 11}

    • 54 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 3, 4, 5, 6}, {0, 2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}, {0, 1, 2, 4, 5, 7}, {0, 1, 3, 4, 5, 7}, {0, 2, 3, 4, 5, 7}, {0, 1, 4, 5, 6, 7}, {0, 2, 4, 5, 6, 7}, {1, 2, 4, 5, 6, 7}, {0, 3, 4, 5, 6, 7}, {1, 3, 4, 5, 6, 7}, {2, 3, 4, 5, 6, 7}, {0, 4, 5, 6, 8, 9}, {3, 4, 5, 7, 8, 9}, {0, 4, 5, 6, 8, 10}, {0, 1, 5, 7, 8, 10}, {3, 4, 5, 7, 8, 10}, {0, 4, 6, 8, 9, 10}, {0, 5, 6, 8, 9, 10}, {3, 4, 7, 8, 9, 10}, {3, 5, 7, 8, 9, 10}, {0, 1, 2, 3, 8, 11}, {0, 1, 3, 6, 8, 11}, {0, 2, 3, 6, 8, 11}, {1, 2, 3, 6, 8, 11}, {0, 4, 5, 6, 8, 11}, {0, 1, 2, 7, 8, 11}, {0, 1, 3, 7, 8, 11}, {0, 2, 3, 7, 8, 11}, {3, 4, 5, 7, 8, 11}, {0, 1, 6, 7, 8, 11}, {0, 2, 6, 7, 8, 11}, {1, 2, 6, 7, 8, 11}, {0, 3, 6, 7, 8, 11}, {1, 3, 6, 7, 8, 11}, {2, 3, 6, 7, 8, 11}, {2, 3, 4, 6, 9, 11}, {0, 4, 5, 6, 9, 11}, {3, 4, 5, 7, 9, 11}, {0, 4, 6, 8, 9, 11}, {0, 5, 6, 8, 9, 11}, {3, 4, 7, 8, 9, 11}, {3, 5, 7, 8, 9, 11}, {0, 4, 5, 6, 10, 11}, {3, 4, 5, 7, 10, 11}, {0, 4, 6, 8, 10, 11}, {0, 5, 6, 8, 10, 11}, {3, 4, 7, 8, 10, 11}, {3, 5, 7, 8, 10, 11}, {0, 4, 6, 9, 10, 11}, {0, 5, 6, 9, 10, 11}, {3, 4, 7, 9, 10, 11}, {3, 5, 7, 9, 10, 11}

    • 300 circuits of size 7:

      {0, 1, 2, 3, 4, 8, 9}, {0, 1, 2, 3, 5, 8, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 2, 3, 4, 5, 8, 9}, {1, 2, 3, 4, 5, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 2, 3, 4, 6, 8, 9}, {1, 2, 3, 4, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {1, 2, 3, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 2, 3, 4, 7, 8, 9}, {0, 1, 2, 5, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 1, 4, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {0, 1, 5, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {1, 2, 5, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 8, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 2, 3, 4, 5, 8, 10}, {1, 2, 3, 4, 5, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {2, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 4, 9, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {2, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {0, 1, 2, 3, 8, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 2, 3, 4, 8, 9, 10}, {1, 2, 3, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {1, 2, 3, 5, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {1, 2, 3, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {2, 3, 4, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {2, 3, 5, 6, 8, 9, 10}, {0, 1, 2, 7, 8, 9, 10}, {0, 1, 3, 7, 8, 9, 10}, {0, 2, 3, 7, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 1, 6, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {1, 2, 6, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {1, 3, 6, 7, 8, 9, 10}, {2, 3, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {1, 4, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 4, 9, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 2, 3, 4, 5, 9, 11}, {1, 2, 3, 4, 5, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 1, 4, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {0, 1, 5, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {1, 4, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 2, 3, 4, 8, 9, 11}, {1, 2, 3, 4, 8, 9, 11}, {0, 1, 2, 5, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 2, 3, 5, 8, 9, 11}, {1, 2, 3, 5, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {2, 3, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 4, 10, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 4, 5, 10, 11}, {0, 1, 3, 4, 5, 10, 11}, {0, 2, 3, 4, 5, 10, 11}, {1, 2, 3, 4, 5, 10, 11}, {0, 1, 3, 4, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 1, 3, 5, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {1, 2, 4, 5, 6, 10, 11}, {1, 3, 4, 5, 6, 10, 11}, {2, 3, 4, 5, 6, 10, 11}, {0, 1, 2, 4, 7, 10, 11}, {0, 1, 3, 4, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {0, 1, 2, 5, 7, 10, 11}, {0, 1, 3, 5, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {0, 1, 4, 5, 7, 10, 11}, {0, 2, 4, 5, 7, 10, 11}, {1, 2, 4, 5, 7, 10, 11}, {0, 1, 4, 6, 7, 10, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {2, 3, 4, 6, 7, 10, 11}, {0, 1, 5, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {1, 4, 5, 6, 7, 10, 11}, {2, 4, 5, 6, 7, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 2, 3, 4, 8, 10, 11}, {1, 2, 3, 4, 8, 10, 11}, {0, 1, 2, 5, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 2, 3, 5, 8, 10, 11}, {1, 2, 3, 5, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 1, 4, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {1, 4, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {1, 5, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 3, 9, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 2, 3, 4, 9, 10, 11}, {1, 2, 3, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 2, 3, 5, 9, 10, 11}, {1, 2, 3, 5, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 2, 3, 7, 9, 10, 11}, {0, 1, 4, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 1, 5, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 1, 6, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 3, 6, 7, 9, 10, 11}, {1, 4, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {1, 5, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}

---

---

55. Graph1255:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {6,7}, {7,10}, {10,11}, {11,8}, {8,9}, {9,6}, {0,6}, {1,7}, {2,8}, {3,9}, {4,10}, {5,11}

• Randomly generated (generic) hyperplane:

  12*a + 6*b + 84*c + 35*d + 50*e + 79*f + 75*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : 0 : 0 : -87/79 : 1]

  [1 : 0 : 0 : -87/35 : 0 : 0 : 1]

  [0 : 0 : 1 : -12/5 : 0 : 0 : 0]

  [0 : 0 : 1 : -84/89 : -84/89 : -84/89 : 84/89]

  [0 : 1 : 0 : 44/89 : -45/89 : 44/89 : -44/89]

  [0 : 1 : 0 : 0 : -1 : 44/79 : 0]

  [1 : 0 : 0 : 0 : 0 : 1 : -91/75]

  [1 : 0 : 0 : -7/3 : 0 : -4/3 : 7/3]

  [0 : 0 : 1 : -1 : -49/129 : -49/129 : 0]

  [0 : 0 : 1 : -1 : -1 : -1 : 16/15]

  [0 : 1 : 0 : -2/13 : 0 : -2/13 : 2/13]

  [0 : 1 : 0 : 0 : -2/43 : -2/43 : 0]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 784 bases, 140 non-bases

  • circuits:

    • 3 circuits of size 4:

      {0, 1, 6, 7}, {2, 3, 8, 9}, {4, 5, 10, 11}

    • 56 circuits of size 6:

      {0, 1, 2, 3, 4, 5}, {0, 1, 2, 3, 6, 8}, {0, 1, 2, 3, 7, 8}, {0, 2, 3, 6, 7, 8}, {1, 2, 3, 6, 7, 8}, {0, 1, 2, 3, 6, 9}, {0, 3, 4, 5, 6, 9}, {0, 1, 2, 3, 7, 9}, {0, 2, 3, 6, 7, 9}, {1, 2, 3, 6, 7, 9}, {0, 1, 2, 6, 8, 9}, {0, 1, 3, 6, 8, 9}, {0, 1, 2, 7, 8, 9}, {0, 1, 3, 7, 8, 9}, {0, 2, 6, 7, 8, 9}, {1, 2, 6, 7, 8, 9}, {0, 3, 6, 7, 8, 9}, {1, 3, 6, 7, 8, 9}, {0, 1, 4, 5, 6, 10}, {1, 2, 3, 4, 7, 10}, {0, 1, 4, 5, 7, 10}, {0, 4, 5, 6, 7, 10}, {1, 4, 5, 6, 7, 10}, {2, 3, 4, 5, 8, 10}, {2, 3, 4, 5, 9, 10}, {3, 4, 6, 7, 9, 10}, {2, 4, 5, 8, 9, 10}, {3, 4, 5, 8, 9, 10}, {0, 1, 4, 5, 6, 11}, {0, 1, 4, 5, 7, 11}, {0, 4, 5, 6, 7, 11}, {1, 4, 5, 6, 7, 11}, {0, 1, 2, 5, 8, 11}, {2, 3, 4, 5, 8, 11}, {2, 3, 4, 5, 9, 11}, {2, 4, 5, 8, 9, 11}, {3, 4, 5, 8, 9, 11}, {0, 5, 6, 8, 9, 11}, {0, 1, 4, 6, 10, 11}, {0, 1, 5, 6, 10, 11}, {0, 1, 4, 7, 10, 11}, {0, 1, 5, 7, 10, 11}, {0, 4, 6, 7, 10, 11}, {1, 4, 6, 7, 10, 11}, {0, 5, 6, 7, 10, 11}, {1, 5, 6, 7, 10, 11}, {2, 3, 4, 8, 10, 11}, {2, 3, 5, 8, 10, 11}, {1, 2, 7, 8, 10, 11}, {2, 3, 4, 9, 10, 11}, {2, 3, 5, 9, 10, 11}, {2, 4, 8, 9, 10, 11}, {3, 4, 8, 9, 10, 11}, {2, 5, 8, 9, 10, 11}, {3, 5, 8, 9, 10, 11}, {6, 7, 8, 9, 10, 11}

    • 384 circuits of size 7:

      {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 4, 5, 6, 8}, {0, 1, 3, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 1, 2, 4, 5, 7, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 4, 5, 6, 9}, {1, 2, 3, 4, 5, 6, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {1, 3, 4, 5, 6, 7, 9}, {2, 3, 4, 5, 6, 7, 9}, {0, 1, 2, 4, 5, 8, 9}, {0, 1, 3, 4, 5, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {1, 3, 4, 5, 6, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {0, 4, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {3, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 4, 6, 10}, {0, 1, 2, 3, 5, 6, 10}, {0, 2, 3, 4, 5, 6, 10}, {1, 2, 3, 4, 5, 6, 10}, {0, 1, 2, 3, 5, 7, 10}, {0, 2, 3, 4, 5, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {2, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 4, 8, 10}, {0, 1, 2, 3, 5, 8, 10}, {0, 1, 2, 4, 5, 8, 10}, {0, 1, 3, 4, 5, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {0, 1, 2, 5, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 4, 9, 10}, {0, 1, 2, 3, 5, 9, 10}, {0, 1, 2, 4, 5, 9, 10}, {0, 1, 3, 4, 5, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {2, 3, 5, 6, 7, 9, 10}, {2, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 4, 8, 9, 10}, {0, 1, 3, 4, 8, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {0, 5, 6, 7, 8, 9, 10}, {1, 5, 6, 7, 8, 9, 10}, {2, 5, 6, 7, 8, 9, 10}, {3, 5, 6, 7, 8, 9, 10}, {4, 5, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 4, 6, 11}, {0, 1, 2, 3, 5, 6, 11}, {0, 2, 3, 4, 5, 6, 11}, {1, 2, 3, 4, 5, 6, 11}, {0, 1, 2, 3, 4, 7, 11}, {0, 1, 2, 3, 5, 7, 11}, {0, 2, 3, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {2, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 4, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, {2, 4, 5, 6, 7, 8, 11}, {3, 4, 5, 6, 7, 8, 11}, {0, 1, 2, 3, 4, 9, 11}, {0, 1, 2, 3, 5, 9, 11}, {0, 1, 2, 4, 5, 9, 11}, {0, 1, 3, 4, 5, 9, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {2, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {2, 3, 5, 6, 7, 9, 11}, {2, 4, 5, 6, 7, 9, 11}, {3, 4, 5, 6, 7, 9, 11}, {0, 1, 2, 4, 8, 9, 11}, {0, 1, 3, 4, 8, 9, 11}, {0, 1, 3, 5, 8, 9, 11}, {0, 1, 4, 5, 8, 9, 11}, {0, 1, 4, 6, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {1, 4, 5, 6, 8, 9, 11}, {0, 1, 4, 7, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {0, 1, 5, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {0, 4, 5, 7, 8, 9, 11}, {1, 4, 5, 7, 8, 9, 11}, {0, 4, 6, 7, 8, 9, 11}, {1, 4, 6, 7, 8, 9, 11}, {2, 4, 6, 7, 8, 9, 11}, {3, 4, 6, 7, 8, 9, 11}, {1, 5, 6, 7, 8, 9, 11}, {2, 5, 6, 7, 8, 9, 11}, {3, 5, 6, 7, 8, 9, 11}, {4, 5, 6, 7, 8, 9, 11}, {0, 1, 2, 3, 4, 10, 11}, {0, 1, 2, 3, 5, 10, 11}, {0, 1, 2, 3, 6, 10, 11}, {0, 2, 3, 4, 6, 10, 11}, {1, 2, 3, 4, 6, 10, 11}, {0, 2, 3, 5, 6, 10, 11}, {1, 2, 3, 5, 6, 10, 11}, {0, 1, 2, 3, 7, 10, 11}, {0, 2, 3, 4, 7, 10, 11}, {0, 2, 3, 5, 7, 10, 11}, {1, 2, 3, 5, 7, 10, 11}, {0, 2, 3, 6, 7, 10, 11}, {1, 2, 3, 6, 7, 10, 11}, {2, 3, 4, 6, 7, 10, 11}, {2, 3, 5, 6, 7, 10, 11}, {0, 1, 2, 3, 8, 10, 11}, {0, 1, 2, 4, 8, 10, 11}, {0, 1, 3, 4, 8, 10, 11}, {0, 1, 3, 5, 8, 10, 11}, {0, 1, 2, 6, 8, 10, 11}, {0, 1, 3, 6, 8, 10, 11}, {0, 2, 3, 6, 8, 10, 11}, {1, 2, 3, 6, 8, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {0, 1, 3, 7, 8, 10, 11}, {0, 2, 3, 7, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {0, 2, 6, 7, 8, 10, 11}, {0, 3, 6, 7, 8, 10, 11}, {1, 3, 6, 7, 8, 10, 11}, {2, 3, 6, 7, 8, 10, 11}, {2, 4, 6, 7, 8, 10, 11}, {3, 4, 6, 7, 8, 10, 11}, {2, 5, 6, 7, 8, 10, 11}, {3, 5, 6, 7, 8, 10, 11}, {0, 1, 2, 3, 9, 10, 11}, {0, 1, 2, 4, 9, 10, 11}, {0, 1, 3, 4, 9, 10, 11}, {0, 1, 2, 5, 9, 10, 11}, {0, 1, 3, 5, 9, 10, 11}, {0, 1, 2, 6, 9, 10, 11}, {0, 1, 3, 6, 9, 10, 11}, {0, 2, 3, 6, 9, 10, 11}, {1, 2, 3, 6, 9, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {0, 1, 2, 7, 9, 10, 11}, {0, 1, 3, 7, 9, 10, 11}, {0, 2, 3, 7, 9, 10, 11}, {1, 2, 3, 7, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 3, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {0, 2, 6, 7, 9, 10, 11}, {1, 2, 6, 7, 9, 10, 11}, {0, 3, 6, 7, 9, 10, 11}, {1, 3, 6, 7, 9, 10, 11}, {2, 3, 6, 7, 9, 10, 11}, {2, 4, 6, 7, 9, 10, 11}, {2, 5, 6, 7, 9, 10, 11}, {3, 5, 6, 7, 9, 10, 11}, {0, 1, 2, 8, 9, 10, 11}, {0, 1, 3, 8, 9, 10, 11}, {0, 1, 4, 8, 9, 10, 11}, {0, 1, 5, 8, 9, 10, 11}, {0, 1, 6, 8, 9, 10, 11}, {0, 2, 6, 8, 9, 10, 11}, {1, 2, 6, 8, 9, 10, 11}, {0, 3, 6, 8, 9, 10, 11}, {1, 3, 6, 8, 9, 10, 11}, {0, 4, 6, 8, 9, 10, 11}, {1, 4, 6, 8, 9, 10, 11}, {1, 5, 6, 8, 9, 10, 11}, {0, 1, 7, 8, 9, 10, 11}, {0, 2, 7, 8, 9, 10, 11}, {0, 3, 7, 8, 9, 10, 11}, {1, 3, 7, 8, 9, 10, 11}, {0, 4, 7, 8, 9, 10, 11}, {1, 4, 7, 8, 9, 10, 11}, {0, 5, 7, 8, 9, 10, 11}, {1, 5, 7, 8, 9, 10, 11}

---

---

56. Graph1256:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,0}, {3,4}, {4,5}, {5,2}, {5,6}, {6,7}, {7,4}, {7,8}, {8,9}, {9,6}, {9,10}, {10,11}, {11,8}, {0,10}, {1,11}

• Randomly generated (generic) hyperplane:

  13*a + 60*b + 73*c + 78*d + 83*e + 72*f + 90*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [0 : 0 : 0 : 1 : 0 : 1/6 : -1]

  [0 : 0 : 0 : 0 : 1 : -83/72 : 0]

  [1 : 0 : 0 : -1 : -97/83 : 1 : 1]

  [1 : 0 : 0 : 13/84 : 0 : -13/84 : -13/84]

  [1 : -13/59 : 13/59 : 0 : 0 : -13/59 : 0]

  [1 : -7/29 : 7/29 : -36/29 : -36/29 : 1 : 36/29]

  [0 : 1 : -66/37 : 66/37 : 66/37 : -29/37 : -66/37]

  [0 : 1 : -132/73 : 0 : 0 : 1 : 0]

  [0 : 0 : 1 : 0 : 73/79 : -73/79 : -73/79]

  [0 : 0 : 1 : -76/39 : -1 : 1 : 1]

  [0 : 0 : 0 : 1 : 0 : 0 : -13/15]

  [0 : 0 : 0 : 0 : 1 : -1 : -11/90]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 666 bases, 258 non-bases

  • circuits:

    • 6 circuits of size 4:

      {0, 1, 2, 3}, {2, 3, 4, 5}, {4, 5, 6, 7}, {6, 7, 8, 9}, {0, 1, 10, 11}, {8, 9, 10, 11}

    • 12 circuits of size 5:

      {0, 1, 2, 4, 5}, {0, 1, 3, 4, 5}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {4, 5, 6, 8, 9}, {4, 5, 7, 8, 9}, {0, 1, 8, 9, 10}, {0, 1, 8, 9, 11}, {0, 2, 3, 10, 11}, {1, 2, 3, 10, 11}, {6, 7, 8, 10, 11}, {6, 7, 9, 10, 11}

    • 24 circuits of size 6:

      {0, 1, 2, 4, 6, 7}, {0, 1, 3, 4, 6, 7}, {0, 1, 2, 5, 6, 7}, {0, 1, 3, 5, 6, 7}, {2, 3, 4, 6, 8, 9}, {2, 3, 5, 6, 8, 9}, {2, 3, 4, 7, 8, 9}, {2, 3, 5, 7, 8, 9}, {0, 1, 6, 7, 8, 10}, {0, 1, 6, 7, 9, 10}, {0, 2, 3, 8, 9, 10}, {1, 2, 3, 8, 9, 10}, {0, 1, 6, 7, 8, 11}, {0, 1, 6, 7, 9, 11}, {0, 2, 3, 8, 9, 11}, {1, 2, 3, 8, 9, 11}, {0, 2, 4, 5, 10, 11}, {1, 2, 4, 5, 10, 11}, {0, 3, 4, 5, 10, 11}, {1, 3, 4, 5, 10, 11}, {4, 5, 6, 8, 10, 11}, {4, 5, 7, 8, 10, 11}, {4, 5, 6, 9, 10, 11}, {4, 5, 7, 9, 10, 11}

    • 240 circuits of size 7:

      {0, 1, 2, 4, 6, 8, 9}, {0, 1, 3, 4, 6, 8, 9}, {0, 1, 2, 5, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 1, 2, 4, 7, 8, 9}, {0, 1, 3, 4, 7, 8, 9}, {0, 1, 2, 5, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {0, 1, 2, 4, 7, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {1, 2, 3, 4, 7, 8, 10}, {0, 1, 2, 5, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {1, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {1, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {1, 2, 3, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {1, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {1, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 2, 3, 4, 6, 9, 10}, {1, 2, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 2, 3, 5, 6, 9, 10}, {1, 2, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 2, 4, 5, 6, 9, 10}, {1, 2, 4, 5, 6, 9, 10}, {0, 3, 4, 5, 6, 9, 10}, {1, 3, 4, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {1, 2, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {1, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {1, 2, 3, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {1, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {1, 3, 4, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {1, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {1, 3, 5, 7, 8, 9, 10}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {0, 1, 4, 5, 6, 8, 11}, {0, 2, 4, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {0, 3, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {0, 1, 2, 4, 7, 8, 11}, {0, 1, 3, 4, 7, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 1, 2, 5, 7, 8, 11}, {0, 1, 3, 5, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 1, 4, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {0, 1, 2, 4, 6, 9, 11}, {0, 1, 3, 4, 6, 9, 11}, {0, 2, 3, 4, 6, 9, 11}, {1, 2, 3, 4, 6, 9, 11}, {0, 1, 2, 5, 6, 9, 11}, {0, 1, 3, 5, 6, 9, 11}, {0, 2, 3, 5, 6, 9, 11}, {1, 2, 3, 5, 6, 9, 11}, {0, 1, 4, 5, 6, 9, 11}, {0, 2, 4, 5, 6, 9, 11}, {1, 2, 4, 5, 6, 9, 11}, {0, 3, 4, 5, 6, 9, 11}, {1, 3, 4, 5, 6, 9, 11}, {0, 1, 2, 4, 7, 9, 11}, {0, 1, 3, 4, 7, 9, 11}, {0, 2, 3, 4, 7, 9, 11}, {1, 2, 3, 4, 7, 9, 11}, {0, 1, 2, 5, 7, 9, 11}, {0, 1, 3, 5, 7, 9, 11}, {0, 2, 3, 5, 7, 9, 11}, {1, 2, 3, 5, 7, 9, 11}, {0, 1, 4, 5, 7, 9, 11}, {0, 2, 4, 5, 7, 9, 11}, {1, 2, 4, 5, 7, 9, 11}, {0, 3, 4, 5, 7, 9, 11}, {1, 3, 4, 5, 7, 9, 11}, {0, 2, 3, 6, 7, 9, 11}, {1, 2, 3, 6, 7, 9, 11}, {0, 2, 4, 6, 7, 9, 11}, {1, 2, 4, 6, 7, 9, 11}, {0, 3, 4, 6, 7, 9, 11}, {1, 3, 4, 6, 7, 9, 11}, {0, 2, 5, 6, 7, 9, 11}, {1, 2, 5, 6, 7, 9, 11}, {0, 3, 5, 6, 7, 9, 11}, {1, 3, 5, 6, 7, 9, 11}, {0, 2, 4, 5, 8, 9, 11}, {1, 2, 4, 5, 8, 9, 11}, {0, 3, 4, 5, 8, 9, 11}, {1, 3, 4, 5, 8, 9, 11}, {0, 2, 4, 6, 8, 9, 11}, {1, 2, 4, 6, 8, 9, 11}, {0, 3, 4, 6, 8, 9, 11}, {1, 3, 4, 6, 8, 9, 11}, {0, 2, 5, 6, 8, 9, 11}, {1, 2, 5, 6, 8, 9, 11}, {0, 3, 5, 6, 8, 9, 11}, {1, 3, 5, 6, 8, 9, 11}, {0, 2, 4, 7, 8, 9, 11}, {1, 2, 4, 7, 8, 9, 11}, {0, 3, 4, 7, 8, 9, 11}, {1, 3, 4, 7, 8, 9, 11}, {0, 2, 5, 7, 8, 9, 11}, {1, 2, 5, 7, 8, 9, 11}, {0, 3, 5, 7, 8, 9, 11}, {1, 3, 5, 7, 8, 9, 11}, {0, 2, 4, 6, 7, 10, 11}, {1, 2, 4, 6, 7, 10, 11}, {0, 3, 4, 6, 7, 10, 11}, {1, 3, 4, 6, 7, 10, 11}, {0, 2, 5, 6, 7, 10, 11}, {1, 2, 5, 6, 7, 10, 11}, {0, 3, 5, 6, 7, 10, 11}, {1, 3, 5, 6, 7, 10, 11}, {0, 2, 4, 6, 8, 10, 11}, {1, 2, 4, 6, 8, 10, 11}, {0, 3, 4, 6, 8, 10, 11}, {1, 3, 4, 6, 8, 10, 11}, {2, 3, 4, 6, 8, 10, 11}, {0, 2, 5, 6, 8, 10, 11}, {1, 2, 5, 6, 8, 10, 11}, {0, 3, 5, 6, 8, 10, 11}, {1, 3, 5, 6, 8, 10, 11}, {2, 3, 5, 6, 8, 10, 11}, {0, 2, 4, 7, 8, 10, 11}, {1, 2, 4, 7, 8, 10, 11}, {0, 3, 4, 7, 8, 10, 11}, {1, 3, 4, 7, 8, 10, 11}, {2, 3, 4, 7, 8, 10, 11}, {0, 2, 5, 7, 8, 10, 11}, {1, 2, 5, 7, 8, 10, 11}, {0, 3, 5, 7, 8, 10, 11}, {1, 3, 5, 7, 8, 10, 11}, {2, 3, 5, 7, 8, 10, 11}, {0, 2, 4, 6, 9, 10, 11}, {1, 2, 4, 6, 9, 10, 11}, {0, 3, 4, 6, 9, 10, 11}, {1, 3, 4, 6, 9, 10, 11}, {2, 3, 4, 6, 9, 10, 11}, {0, 2, 5, 6, 9, 10, 11}, {1, 2, 5, 6, 9, 10, 11}, {0, 3, 5, 6, 9, 10, 11}, {1, 3, 5, 6, 9, 10, 11}, {2, 3, 5, 6, 9, 10, 11}, {0, 2, 4, 7, 9, 10, 11}, {1, 2, 4, 7, 9, 10, 11}, {0, 3, 4, 7, 9, 10, 11}, {1, 3, 4, 7, 9, 10, 11}, {2, 3, 4, 7, 9, 10, 11}, {0, 2, 5, 7, 9, 10, 11}, {1, 2, 5, 7, 9, 10, 11}, {0, 3, 5, 7, 9, 10, 11}, {1, 3, 5, 7, 9, 10, 11}, {2, 3, 5, 7, 9, 10, 11}

---

---

57. Graph1257:

• Edges of graph:

  {0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {2,10}, {3,9}, {6,9}, {7,10}, {4,5}, {5,10}, {5,6}, {1,8}, {8,9}, {8,7}, {0,11}, {7,11}, {11,6}

• Randomly generated (generic) hyperplane:

  76*a + 53*b + 12*c + 31*d + 31*e + 78*f + 48*g = 0

• Coordinates of the 12 points in the hyperplane section:

  [1 : 0 : 0 : 0 : -76 : 76 : -76]

  [1 : 0 : 0 : -38/31 : -38/31 : 0 : 0]

  [1 : -23/22 : 0 : 1 : -1/22 : 0 : -23/22]

  [1 : 1 : 135/64 : -71/64 : -7/64 : -135/64 : 1]

  [1 : -77/65 : -77/65 : 0 : 1 : -1 : 1]

  [0 : 1 : 101/36 : 0 : 0 : 0 : -65/36]

  [0 : 0 : 1 : 0 : 0 : 0 : -1/4]

  [0 : 0 : 0 : 0 : 1 : -31/78 : 0]

  [0 : 0 : 0 : 1 : 1 : -31/39 : 0]

  [0 : 0 : 1 : -3/35 : -3/35 : -3/35 : 0]

  [0 : 1 : 0 : 0 : -101/31 : 0 : 1]

  [0 : 0 : 0 : 0 : 1 : -1 : 47/48]

• Matroid of rank 6 on base set {0, 1,..., 11}:

  • 834 bases, 90 non-bases

  • circuits:

    • 9 circuits of size 5:

      {0, 1, 2, 3, 4}, {3, 4, 5, 6, 9}, {1, 2, 3, 8, 9}, {2, 3, 4, 5, 10}, {1, 2, 7, 8, 10}, {0, 4, 5, 6, 11}, {0, 1, 7, 8, 11}, {6, 7, 8, 9, 11}, {5, 6, 7, 10, 11}

    • 27 circuits of size 6:

      {0, 1, 2, 4, 8, 9}, {0, 1, 3, 4, 8, 9}, {0, 2, 3, 4, 8, 9}, {0, 1, 6, 7, 8, 9}, {0, 1, 2, 3, 5, 10}, {0, 1, 2, 4, 5, 10}, {0, 1, 3, 4, 5, 10}, {0, 4, 5, 6, 7, 10}, {2, 3, 4, 6, 9, 10}, {2, 3, 5, 6, 9, 10}, {2, 4, 5, 6, 9, 10}, {1, 2, 3, 7, 9, 10}, {1, 3, 7, 8, 9, 10}, {2, 3, 7, 8, 9, 10}, {5, 6, 7, 8, 9, 10}, {0, 3, 4, 5, 9, 11}, {0, 3, 4, 6, 9, 11}, {0, 3, 5, 6, 9, 11}, {0, 1, 6, 7, 9, 11}, {0, 1, 6, 8, 9, 11}, {0, 1, 2, 7, 10, 11}, {0, 4, 5, 7, 10, 11}, {0, 4, 6, 7, 10, 11}, {0, 1, 2, 8, 10, 11}, {0, 2, 7, 8, 10, 11}, {5, 6, 8, 9, 10, 11}, {5, 7, 8, 9, 10, 11}

    • 477 circuits of size 7:

      {0, 1, 2, 3, 5, 6, 7}, {0, 1, 2, 4, 5, 6, 7}, {0, 1, 3, 4, 5, 6, 7}, {0, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7}, {0, 1, 2, 3, 5, 6, 8}, {0, 1, 2, 4, 5, 6, 8}, {0, 1, 3, 4, 5, 6, 8}, {0, 2, 3, 4, 5, 6, 8}, {1, 2, 3, 4, 5, 6, 8}, {0, 1, 2, 3, 5, 7, 8}, {0, 1, 2, 4, 5, 7, 8}, {0, 1, 3, 4, 5, 7, 8}, {0, 2, 3, 4, 5, 7, 8}, {1, 2, 3, 4, 5, 7, 8}, {0, 1, 2, 3, 6, 7, 8}, {0, 1, 2, 4, 6, 7, 8}, {0, 1, 3, 4, 6, 7, 8}, {0, 2, 3, 4, 6, 7, 8}, {1, 2, 3, 4, 6, 7, 8}, {0, 1, 2, 5, 6, 7, 8}, {0, 1, 3, 5, 6, 7, 8}, {0, 2, 3, 5, 6, 7, 8}, {1, 2, 3, 5, 6, 7, 8}, {0, 1, 4, 5, 6, 7, 8}, {0, 2, 4, 5, 6, 7, 8}, {1, 2, 4, 5, 6, 7, 8}, {0, 3, 4, 5, 6, 7, 8}, {1, 3, 4, 5, 6, 7, 8}, {2, 3, 4, 5, 6, 7, 8}, {0, 1, 2, 3, 5, 6, 9}, {0, 1, 2, 4, 5, 6, 9}, {0, 1, 2, 3, 5, 7, 9}, {0, 1, 2, 4, 5, 7, 9}, {0, 1, 3, 4, 5, 7, 9}, {0, 2, 3, 4, 5, 7, 9}, {1, 2, 3, 4, 5, 7, 9}, {0, 1, 2, 3, 6, 7, 9}, {0, 1, 2, 4, 6, 7, 9}, {0, 1, 3, 4, 6, 7, 9}, {0, 2, 3, 4, 6, 7, 9}, {1, 2, 3, 4, 6, 7, 9}, {0, 1, 2, 5, 6, 7, 9}, {0, 1, 3, 5, 6, 7, 9}, {0, 2, 3, 5, 6, 7, 9}, {1, 2, 3, 5, 6, 7, 9}, {0, 1, 4, 5, 6, 7, 9}, {0, 2, 4, 5, 6, 7, 9}, {1, 2, 4, 5, 6, 7, 9}, {0, 1, 2, 5, 6, 8, 9}, {0, 1, 3, 5, 6, 8, 9}, {0, 2, 3, 5, 6, 8, 9}, {0, 1, 4, 5, 6, 8, 9}, {0, 2, 4, 5, 6, 8, 9}, {1, 2, 4, 5, 6, 8, 9}, {0, 1, 2, 5, 7, 8, 9}, {0, 1, 3, 5, 7, 8, 9}, {0, 2, 3, 5, 7, 8, 9}, {0, 1, 4, 5, 7, 8, 9}, {0, 2, 4, 5, 7, 8, 9}, {1, 2, 4, 5, 7, 8, 9}, {0, 3, 4, 5, 7, 8, 9}, {1, 3, 4, 5, 7, 8, 9}, {2, 3, 4, 5, 7, 8, 9}, {0, 2, 3, 6, 7, 8, 9}, {0, 2, 4, 6, 7, 8, 9}, {1, 2, 4, 6, 7, 8, 9}, {0, 3, 4, 6, 7, 8, 9}, {1, 3, 4, 6, 7, 8, 9}, {2, 3, 4, 6, 7, 8, 9}, {0, 2, 5, 6, 7, 8, 9}, {1, 2, 5, 6, 7, 8, 9}, {0, 3, 5, 6, 7, 8, 9}, {1, 3, 5, 6, 7, 8, 9}, {2, 3, 5, 6, 7, 8, 9}, {0, 4, 5, 6, 7, 8, 9}, {1, 4, 5, 6, 7, 8, 9}, {2, 4, 5, 6, 7, 8, 9}, {0, 1, 2, 3, 6, 7, 10}, {0, 1, 2, 4, 6, 7, 10}, {0, 1, 3, 4, 6, 7, 10}, {0, 2, 3, 4, 6, 7, 10}, {1, 2, 3, 4, 6, 7, 10}, {0, 1, 2, 5, 6, 7, 10}, {0, 1, 3, 5, 6, 7, 10}, {0, 2, 3, 5, 6, 7, 10}, {1, 2, 3, 5, 6, 7, 10}, {1, 2, 4, 5, 6, 7, 10}, {1, 3, 4, 5, 6, 7, 10}, {0, 1, 2, 3, 6, 8, 10}, {0, 1, 2, 4, 6, 8, 10}, {0, 1, 3, 4, 6, 8, 10}, {0, 2, 3, 4, 6, 8, 10}, {1, 2, 3, 4, 6, 8, 10}, {0, 1, 2, 5, 6, 8, 10}, {0, 1, 3, 5, 6, 8, 10}, {0, 2, 3, 5, 6, 8, 10}, {1, 2, 3, 5, 6, 8, 10}, {0, 1, 4, 5, 6, 8, 10}, {0, 2, 4, 5, 6, 8, 10}, {1, 2, 4, 5, 6, 8, 10}, {0, 3, 4, 5, 6, 8, 10}, {1, 3, 4, 5, 6, 8, 10}, {0, 1, 3, 4, 7, 8, 10}, {0, 2, 3, 4, 7, 8, 10}, {0, 1, 3, 5, 7, 8, 10}, {0, 2, 3, 5, 7, 8, 10}, {0, 1, 4, 5, 7, 8, 10}, {0, 2, 4, 5, 7, 8, 10}, {0, 3, 4, 5, 7, 8, 10}, {1, 3, 4, 5, 7, 8, 10}, {0, 1, 3, 6, 7, 8, 10}, {0, 2, 3, 6, 7, 8, 10}, {0, 1, 4, 6, 7, 8, 10}, {0, 2, 4, 6, 7, 8, 10}, {0, 3, 4, 6, 7, 8, 10}, {1, 3, 4, 6, 7, 8, 10}, {2, 3, 4, 6, 7, 8, 10}, {0, 1, 5, 6, 7, 8, 10}, {0, 2, 5, 6, 7, 8, 10}, {0, 3, 5, 6, 7, 8, 10}, {1, 3, 5, 6, 7, 8, 10}, {2, 3, 5, 6, 7, 8, 10}, {1, 4, 5, 6, 7, 8, 10}, {2, 4, 5, 6, 7, 8, 10}, {3, 4, 5, 6, 7, 8, 10}, {0, 1, 2, 3, 6, 9, 10}, {0, 1, 2, 4, 6, 9, 10}, {0, 1, 3, 4, 6, 9, 10}, {0, 1, 2, 5, 6, 9, 10}, {0, 1, 3, 5, 6, 9, 10}, {0, 1, 4, 5, 6, 9, 10}, {0, 1, 2, 4, 7, 9, 10}, {0, 1, 3, 4, 7, 9, 10}, {0, 2, 3, 4, 7, 9, 10}, {0, 1, 2, 5, 7, 9, 10}, {0, 1, 3, 5, 7, 9, 10}, {0, 2, 3, 5, 7, 9, 10}, {0, 1, 4, 5, 7, 9, 10}, {0, 2, 4, 5, 7, 9, 10}, {1, 2, 4, 5, 7, 9, 10}, {0, 3, 4, 5, 7, 9, 10}, {1, 3, 4, 5, 7, 9, 10}, {0, 1, 2, 6, 7, 9, 10}, {0, 1, 3, 6, 7, 9, 10}, {0, 2, 3, 6, 7, 9, 10}, {0, 1, 4, 6, 7, 9, 10}, {0, 2, 4, 6, 7, 9, 10}, {1, 2, 4, 6, 7, 9, 10}, {0, 3, 4, 6, 7, 9, 10}, {1, 3, 4, 6, 7, 9, 10}, {0, 1, 5, 6, 7, 9, 10}, {0, 2, 5, 6, 7, 9, 10}, {1, 2, 5, 6, 7, 9, 10}, {0, 3, 5, 6, 7, 9, 10}, {1, 3, 5, 6, 7, 9, 10}, {1, 4, 5, 6, 7, 9, 10}, {0, 1, 2, 5, 8, 9, 10}, {0, 1, 3, 5, 8, 9, 10}, {0, 2, 3, 5, 8, 9, 10}, {0, 1, 4, 5, 8, 9, 10}, {0, 2, 4, 5, 8, 9, 10}, {1, 2, 4, 5, 8, 9, 10}, {0, 3, 4, 5, 8, 9, 10}, {1, 3, 4, 5, 8, 9, 10}, {0, 1, 2, 6, 8, 9, 10}, {0, 1, 3, 6, 8, 9, 10}, {0, 2, 3, 6, 8, 9, 10}, {0, 1, 4, 6, 8, 9, 10}, {0, 2, 4, 6, 8, 9, 10}, {1, 2, 4, 6, 8, 9, 10}, {0, 3, 4, 6, 8, 9, 10}, {1, 3, 4, 6, 8, 9, 10}, {0, 1, 5, 6, 8, 9, 10}, {0, 2, 5, 6, 8, 9, 10}, {1, 2, 5, 6, 8, 9, 10}, {0, 3, 5, 6, 8, 9, 10}, {1, 3, 5, 6, 8, 9, 10}, {0, 4, 5, 6, 8, 9, 10}, {1, 4, 5, 6, 8, 9, 10}, {0, 1, 4, 7, 8, 9, 10}, {0, 2, 4, 7, 8, 9, 10}, {0, 3, 4, 7, 8, 9, 10}, {0, 1, 5, 7, 8, 9, 10}, {0, 2, 5, 7, 8, 9, 10}, {0, 3, 5, 7, 8, 9, 10}, {0, 4, 5, 7, 8, 9, 10}, {1, 4, 5, 7, 8, 9, 10}, {2, 4, 5, 7, 8, 9, 10}, {3, 4, 5, 7, 8, 9, 10}, {0, 2, 6, 7, 8, 9, 10}, {0, 3, 6, 7, 8, 9, 10}, {0, 4, 6, 7, 8, 9, 10}, {1, 4, 6, 7, 8, 9, 10}, {2, 4, 6, 7, 8, 9, 10}, {3, 4, 6, 7, 8, 9, 10}, {0, 1, 2, 3, 5, 6, 11}, {1, 2, 3, 4, 5, 6, 11}, {0, 1, 2, 3, 5, 7, 11}, {0, 1, 2, 4, 5, 7, 11}, {0, 1, 3, 4, 5, 7, 11}, {0, 2, 3, 4, 5, 7, 11}, {1, 2, 3, 4, 5, 7, 11}, {0, 1, 2, 3, 6, 7, 11}, {0, 1, 2, 4, 6, 7, 11}, {0, 1, 3, 4, 6, 7, 11}, {0, 2, 3, 4, 6, 7, 11}, {1, 2, 3, 4, 6, 7, 11}, {0, 1, 2, 5, 6, 7, 11}, {0, 1, 3, 5, 6, 7, 11}, {0, 2, 3, 5, 6, 7, 11}, {1, 2, 3, 5, 6, 7, 11}, {1, 2, 4, 5, 6, 7, 11}, {1, 3, 4, 5, 6, 7, 11}, {2, 3, 4, 5, 6, 7, 11}, {0, 1, 2, 3, 5, 8, 11}, {0, 1, 2, 4, 5, 8, 11}, {0, 1, 3, 4, 5, 8, 11}, {0, 2, 3, 4, 5, 8, 11}, {1, 2, 3, 4, 5, 8, 11}, {0, 1, 2, 3, 6, 8, 11}, {0, 1, 2, 4, 6, 8, 11}, {0, 1, 3, 4, 6, 8, 11}, {0, 2, 3, 4, 6, 8, 11}, {1, 2, 3, 4, 6, 8, 11}, {0, 1, 2, 5, 6, 8, 11}, {0, 1, 3, 5, 6, 8, 11}, {0, 2, 3, 5, 6, 8, 11}, {1, 2, 3, 5, 6, 8, 11}, {1, 2, 4, 5, 6, 8, 11}, {1, 3, 4, 5, 6, 8, 11}, {2, 3, 4, 5, 6, 8, 11}, {0, 2, 3, 4, 7, 8, 11}, {1, 2, 3, 4, 7, 8, 11}, {0, 2, 3, 5, 7, 8, 11}, {1, 2, 3, 5, 7, 8, 11}, {0, 2, 4, 5, 7, 8, 11}, {1, 2, 4, 5, 7, 8, 11}, {0, 3, 4, 5, 7, 8, 11}, {1, 3, 4, 5, 7, 8, 11}, {2, 3, 4, 5, 7, 8, 11}, {0, 2, 3, 6, 7, 8, 11}, {1, 2, 3, 6, 7, 8, 11}, {0, 2, 4, 6, 7, 8, 11}, {1, 2, 4, 6, 7, 8, 11}, {0, 3, 4, 6, 7, 8, 11}, {1, 3, 4, 6, 7, 8, 11}, {2, 3, 4, 6, 7, 8, 11}, {0, 2, 5, 6, 7, 8, 11}, {1, 2, 5, 6, 7, 8, 11}, {0, 3, 5, 6, 7, 8, 11}, {1, 3, 5, 6, 7, 8, 11}, {2, 3, 5, 6, 7, 8, 11}, 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