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Modular Reduction in Abstract Polytopes

Published online by Cambridge University Press:  20 November 2018

B. Monson and
Egon Schulte
B. Monson
Affiliation:
University of New Brunswick, Fredericton, NB E3B 5A3 e-mail: bmonson@unb.ca
Egon Schulte
Affiliation:
Northeastern University, Boston, MA, U.S.A. 02115 e-mail: schulte@neu.edu
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Abstract

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The paper studies modular reduction techniques for abstract regular and chiral polytopes, with two purposes in mind: first, to survey the literature about modular reduction in polytopes; and second, to apply modular reduction, with moduli given by primes in $\mathbb{Z}\left[ \tau\right]$ (with $\tau$ the golden ratio), to construct new regular 4-polytopes of hyperbolic types $\{3,\,5,\,3\}$ and $\{5,\,3,\,5\}$ with automorphism groups given by finite orthogonal groups.

Keywords

51M2020F55abstract polytopesregular and chiralCoxeter groupsmodular reduction

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 52 , Issue 3 , 01 September 2009, pp. 435 - 450
Copyright
Copyright © Canadian Mathematical Society 2009

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