aequationes mathematicae

, Volume 57, Issue 1, pp 108–120

More on quotient polytopes

  • M. I. Hartley

DOI: 10.1007/s000100050073

Cite this article as:
Hartley, M. Aequ. math. (1999) 57: 108. doi:10.1007/s000100050073


In an earlier paper, it was shown that every abstract polytope is a quotient \( {\cal Q} = {\cal M}(W)/N \) of some regular polytope \( {\cal M}(W) \) whose automorphism group is W, by a subgroup N of W. In this paper, attention is focussed on the quotient \( {\cal Q} \), and various important structures relating to polytopes are described in terms of N′, the stabilizer of a flag of the quotient under an action of W (the ‘flag action’). It is pointed out how N′ may be assumed without loss of generality to equal N. The paper also shows what properties of N′ yield polytopes which are regular, section regular, chiral, locally regular, or locally universal. The aim is to make it more practical to study non-regular polytopes in terms of group theory.

Keywords. Abstract polytopes, flag action, quotient polytopes, Coxeter groups, C-groups. 

Copyright information

© Birkhäuser Verlag, Basel, 1999

Authors and Affiliations

  • M. I. Hartley
    • 1
  1. 1.Sepang Institute of Technology, Level 5, Klang Parade, 2112 Jalan Meru, Klang, 41050, Selangor, Malaysia, e-mail:

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