A theorem by [GGMS] says that a polytope with vertices in \( \{0,1\}^n \) is a matroid polytope if and only if every edge of the polytope is parallel to \( e_i - e_j \) for some \( i \) and \( j \).

My question is, has this been implemented somewhere in polymake? Specifically, I would like to be able to ask if a polytope is a matroid polytope or not.

Additionally, we say a regular subdivision is a matroid subdivision if every polytope in the subdivision is a matroid polytope. I would like to be able to test if a regular subdivision is a matroid subdivision or not as well.