Discrete & Computational Geometry

, Volume 21, Issue 2, pp 289–298

All Polytopes Are Quotients, and Isomorphic Polytopes Are Quotients by Conjugate Subgroups

  • M. I. Hartley

DOI: 10.1007/PL00009422

Cite this article as:
Hartley, M. Discrete Comput Geom (1999) 21: 289. doi:10.1007/PL00009422


In this paper it is shown that any (abstract) polytope \(\cal P\) is a quotient of a regular polytope \(\cal M\) by some subgroup N of the automorphism group W of \(\cal M\) , and also that isomorphic polytopes are quotients of \(\cal M\) by conjugate subgroups of W . This extends work published in 1980 by Kato, who proved these results for a restricted class of polytopes which he called ``regular''. The methods used here are more elementary, and treat the problem in a purely nongeometric manner.

Copyright information

© 1998 Springer-Verlag New York Inc.

Authors and Affiliations

  • M. I. Hartley
    • 1
  1. 1.University of Western Australia, Nedlands, WA 6907, Australia hartley@maths.uwa.edu.auAU
  2. 2.Current Address: Sepang Institute of Technology, Level 5, Klang Parade, 2112 Jalan Meru, 41050 Klang, Selangor Darul Ehsan, Malaysia. hartleym@sit.edu.my.MY