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格多胞体（lattice polytope）的多宽度（multi-width）刻画了其关于一组线性无关对偶向量（dual vectors）的三个最小格宽度。本数据集包含满足多宽度为$(2,w_2,w_3)$的格四面体（lattice tetrahedra），其中$w_2$不超过10，$w_3$不超过12。构建本数据集所用算法的详细信息，请参见文献[Ham24]。 若您使用本数据集，请同时引用[Ham24]以及本数据集的DOI：doi:10.5281/zenodo.7802562 本数据集收录于文件"width_2_tetrahedra.txt"，其中包含每个格四面体的顶点坐标，以及每个四面体的唯一标识符（ID）。ID的前六位代表该四面体的多宽度，剩余四位用于区分具有相同多宽度的格四面体。所有条目均按ID排序，总计34931条。 本记录为第二版，较第一版新增了30117个格四面体。第一版（V1）中的格四面体ID，与第二版（V2）中的对应条目ID仅存在一处差异：在原ID的前六位与后三位之间额外插入了一个零。 示例条目 ID: 0202020001 Vertices: [[0, 0, 0], [1, 0, 0], [0, 1, 0], [2, 3, 10]] 参考文献 [Ham24] 格特鲁德·哈默（Girtrude Hamm），《基于多宽度对宽度1格四面体的分类》，《离散计算几何（Discrete Comput Geom）》2024年。https://doi.org/10.1007/s00454-024-00659-5