A recursive Algorithm for the k-face Numbers of Wythoffian-n-polytopes Constructed from Regular Polytopes

Abstract

In this paper, an n-dimensional polytope is called Wythoffian if it is derived by the Wythoff construction from an n-dimensional regular polytope whose finite reflection group belongs to A_n, B_n, C_n, F₄, G₂, H₃, H₄ or I₂(p). Based on combinatorial and topological arguments, we give a matrix-form recursive algorithm that calculates the number of k-faces (k =0, 1,..., n) of all the Wythoffian-n-polytopes using Schläfli-Wythoff symbols. The correctness of the algorithm is reconfirmed by the method of exhaustion using a computer.