Polytopes

The following is a collection of polytopes on which we tested our volume computation codes. The polytopes are given in the file format specified by David Avis and Komei Fukuda. We included the .ext- and .ine-files (if this sounds weird to you, you had better read the Vinci documentation, it comprises a description of the file format). The data are split into separate files, each of them corresponding to a different problem class.

• cube: hypercubes with -1 and 1 as vertex coordinates, in dimension 2 to 14.
• cross: cross polytopes, the duals of the cubes above, also in dimension 2 to 14.
• rh: polytopes constructed by randomly choosing hyperplanes tangent to the sphere; after unpacking, files rh_d_m will be created, where d stands for the dimension and m for the number of hyperplanes.
• rv: dually to the previous category these polytopes have vertices randomly distributed on the sphere.
• cc: cc_8_7 to cc_8_11, the product of two cyclic polyhedra with seven to eleven vertices, each in dimension 4. The final dimension is therefore 8.
• ccp: complete cut polytopes on five to seven vertices. The polytopes have been scaled by 2 and then translated by 1 to contain the origin in their interor. So their vertices have coordinates +1 and -1 now.
• metric: after expansion, contains facets of the fourth (Fm_4) to sixth (Fm_6) metric polytope.