Topcom http://www.rambau.wm.uni-bayreuth.de/TOPCOM/ is mathematical software written by Jorg Rambau for computing and manipulating triangulations of polytopes and chirotopes.
This package implements two key functions from the topcom package isRegularTriangulation checks whether a triangulation of a point set is a regular triangulation, and regularFineTriangulation (missing documentation) computes a triangulation which involves all lattice points of a polytope.
There are many other functions available in Topcom. If you wish any of these implemented, or you would like to contribute such an implementation, please contact the author.