This research is concerned primarily with the combinatorics of convex polytopes, including questions about barycentric subsivisions, facial enumerations, and other combinatorial questions about the special classes of k-simplicial and h- simplicial polytopes. Knowing how many faces there can be in a polytope has turned out to be of interest to some computer scientists and geometers. Such knowledge is important in finding convenient data structures for storing geometric data and in analyzing the complexity of algorithms.
