The Vertex-preserving Simplicial Dissectionof Convex Polytopes
Yan Ping · Shuxue de shijian yu renshi · 2008
Via the new concepts of sunny facets,shady facets and flat projective facets of a convex polytope to an outer point and two shield lemmas,it is proved that any n-polytope in Rn can be dissected into a finite union of n-simplices with the vertices coincide with the original polytope and no pair of small simplices has an interior point in common.This improves the corresponding results of relevant literature,and a new dissection toolfor the simplicial method is supplied.