CLEAVED ABSTRACT POLYTOPES

摘要

From a given abstract n-polytope P and a given integer k we derive two abstract polytopes Cl_k (P) and fCl_k (P) of ranks n and n-1, respectively. These constructions generalise the truncation of convex polyhedra and the dual of a geometric construction yielding Petrie's polyhedron {4,6 | 4}. We determine sufficient and necessary conditions to guarantee that Cl_k (P) and fCl_k (P) are regular.