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 10 and \(w_3\) is at most 12. For details of the algorithm used to create this data see [Ham24].

If you make use of this data, please cite [Ham24] and the DOI for this data:

doi:10.5281/zenodo.7802562

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 four differentiate between tetrahedra with the same multi-width. Entries are ordered by their ID. There are 34,931 entries in total.

This is the second version of this record, containing an additional 30,117 tetrahedra. The ID of a tetrahedron in V1 is the same as its entry in V2 only with an additional zero between the first six and last three digits.

Example entry

ID: 0202020001Vertices: [[0, 0, 0], [1, 0, 0], [0, 1, 0], [2, 3, 10]]

References

[Ham24] Girtrude Hamm, Classification of width 1 lattice tetrahedra by their multi-width. Discrete Comput Geom (2024). https://doi.org/10.1007/s00454-024-00659-5