Counting polytopes via the Radon complex

摘要

A convex polytope is the convex hull of a finite set of points. We introduce the Radon complex of a polytope-a subcomplex of an appropriate hypercube which encodes all Radon partitions of the polytope's vertex set. By proving that such a complex, when the vertices of the polytope are in general position, is homeomorphic to a sphere, we find an explicit formula to count the number of d-dimensional polytope types with d + 3 vertices in general position. (C) 2004 Elsevier Inc. All rights reserved.