Dataset of "small" lattice polytopes

Resulting dataset from the paper Enumeration of Lattice Polytopes by Their Volume.

edit: it is recommended to download the dataset from Zenodo as it is compressed and requires no extra postprocessing due to github size limit

Cite as

Balletti, G. Enumeration of Lattice Polytopes by Their Volume. Discrete Comput Geom 65, 1087–1122 (2021). [doi, arXiv].

Content

It contains the following complete datasets of lattice polytopes, see the paper for additional details.

• 2-simplices up to volume 1000
• 3-simplices up to volume 1000
• 4-simplices up to volume 24
• 5-simplices up to volume 20
• 6-simplices up to volume 16
• 2-polytopes up to volume 50
• 3-polytopes up to volume 36
• 4-polytopes up to volume 24
• 5-polytopes up to volume 20
• 6-polytopes up to volume 16
• Smooth 2-polytopes up to volume 50
• Smooth 3-polytopes up to volume 36
• Smooth 4-polytopes up to volume 24
• Smooth 5-polytopes up to volume 20
• Smooth 6-polytopes up to volume 16

Be careful

• Each polytope is saved as the sequence of its vertices, as in the following example.

  [[0,0],[1,0],[0,1],[1,1]]
  

• Simplices and polytopes are listed by their volume, e.g. the file 4-polytopes/v12.txt contains all the 4-polytopes having normalized volume equal to 12 (one representative for each equivalence class).

• Each file ends with an empty line.

• In order to keep each file smaller than 50Mb, the files v34.txt, v35.txt and v36.txt in data/3-polytopes/ are respectively split in two or three files, e.g v34a.txt and v34b.txt. Once downloaded they can be joined using cat.

    cat v34a.txt v34b.txt > v34.txt