Width 2 tetrahedra with small multi-width

The multi-width of a lattice polytope encodes its three smallest lattice widths with respect to linearly independent dual vectors. This is a data set consisting of lattice tetrahedra with multi-width \((2,w_2,w_3)\) where \(w_2\) is at most 5 and \(w_3\) is at most 12. For details of the algorithm used to create this data see [Ham23].

If you make use of this data, please cite [Ham23] and the DOI for this data:

doi:10.5281/zenodo.7802563

The data consists of a file "width_2_tetrahedra.txt" which contains the vertices of each tetrahedron along with a unique ID for each. The first six digits of the ID represent the multi-width of the tetrahedron and the remaining three differentiate between tetrahedra with the same multi-width. Entries are ordered by their ID.

There are 4814 entries in total. When the second width is 2 (resp. 3, 4, 5) the third width is bounded by 12 (resp. 12, 11, 5).

Example entry

ID: 020202001
Vertices: [[0, 0, 0], [1, 0, 0], [0, 1, 0], [2, 3, 10]]

References

[Ham23] Girtrude Hamm, Classification of width 1 lattice tetrahedra by their multi-width. arXiv:2304.03627 [math.CO], 2023