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Rubik's Cube provides a lot of useful tool for manipulating rubik's cube's position.

Running it actually counts the number of equivalence class of last layer positions, considerating that :

  • doing a rotation of the upper face before applying an algorithm doesn't change its class
  • same for doing the rotation after applying the algorithm
  • an algorithm and its reverse are in the same class
  • an algorithm and its symmetry are in the same class
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