Journal of Information Processing
Online ISSN : 1882-6652
ISSN-L : 1882-6652
A recursive Algorithm for the k-face Numbers of Wythoffian-n-polytopes Constructed from Regular Polytopes
Jin AkiyamaSin HitotumatuMotonaga IshiiAkihiro MatsuuraIkuro SatoShun Toyoshima
Author information
JOURNALS FREE ACCESS

2017 Volume 25 Pages 528-536

Details
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 An, Bn, Cn, 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.

Information related to the author
© 2017 by the Information Processing Society of Japan
Previous article Next article
feedback
Top