A matroid polytope is a combinatorial analogue of a convex polytope, namely an oriented matroid that satisfies certain "convexity" conditions.
The programs here will allow you to give a partial description of either the "positional" or the "boundary" information, and search for matroid polytopes consistent with this information.
The software is available from http://www.cs.unb.ca/~bremner/software/mpc/mpc-0.6.tar.gz
2008/05/12 : Release 0.6 contains minor bug fixes
2006/09/27 : Release 0.5 contains important bug fixes to the generation of Grassman-Pluecker relations. Users of previous versions should upgrade.
Some slides from the most recent talk I gave on this topic are available as http://www.cs.unb.ca/~bremner/research/talks/mpc.pdf
This software is an outgrowth of research with Fred Holt, Victor Klee, and Eric Babson.