Polymake Data Set
Triangulations of 3- and 4-dimensional simplicial smooth Fano polytopes

The polytopes are saved into the files "fano_polytopes_3.tgz" and "fano_polytopes_4.tgz". The folder "3D" contains all triangulations for 3-dimensional fano polytopes, the folder "4D" those for 4-dimensional polytopes. The subfolder "Fano_i" is the unique folder containing the data of the polytope with index "i" of the parents folders dimension (e.g. "/4D/Fano_24/" contains all files containing data for the 4-dimensional fano polytope with indes 24 in the array of polytopes from the "fano_polytopes_4.tgz" file).
The data is split into triangulations with and without the origin. Every file that uses the origin uses the suffix "_0" (e.g. FILENAME_0.xml). The origin is ALWAYS labeled with the biggest indice (e.g. let V = { v_1, ..., v_n } be the set of vertices of a polytope, then the point set including the origin is {v_1, ..., v_n, v_{n+1} } where v_{n+1} is the origin).

triang.xml/triang_0.xml
contains one triangulation of each symmetrieclass.

sym_class_i.xml/sym_class_i_0.xml
contains all triangulations of the ith symmetrieclass.

foldable.xml/foldable_0.xlm
contains the foldable triangulations.