I'm interested in looking at the uniform convex polytopes in various dimensions: the 18 Platonic and Archimedean solids, the 64 uniform polychora, the 105 known uniform 5-polytopes, etc. Is there some convenient way to construct or load these in polymake without manually entering coordinates?
Failing that, Wikipedia provides coordinates for all these. Usually, these are given like "All permutions of (±1,±1,0)". Is there a convenient way to input all the permutations and sign-alternations of a list as the coordinates of a polytope?
One thing I'm looking at is whether the symmetry group is transitive on the faces of each dimension. The properties TRANSVERSALS and TRANSVERSAL_SIZES of GroupOfPolytope seem interesting for this, but I don't understand what they mean. Can someone explain them?
The properties N_ORBITS_OF_VERTICES and N_ORBITS_OF_FACETS answer my question for vertices and facets. Is there a way to get this information for other dimensions?