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Locally Toroidal Polytopes and Modular Linear Groups

By B. Monson and Egon Schulte

Abstract

When the standard representation of a crystallographic Coxeter group G (with string diagram) is reduced modulo the integer d>1, one obtains a finite group G^d which is often the automorphism group of an abstract regular polytope. Building on earlier work in the case that d is an odd prime, we here develop methods to handle composite moduli and completely describe the corresponding modular polytopes when G is of spherical or Euclidean type. Using a modular variant of the quotient criterion, we then describe the locally toroidal polytopes provided by our construction, most of which are new.Comment: 21 pages (to appear in Discrete Mathematics

Topics: Mathematics - Combinatorics, Mathematics - Metric Geometry, 51M20, 20F55
Year: 2008
OAI identifier: oai:arXiv.org:0805.3479

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