Locally toroidal polytopes and modular linear groups

When the standard representation of a crystallographic Coxeter group G (with string diagram) is reduced modulo the integer d 2, one obtains a finite group Gd 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. s: locally toroidal polytopes, abstract regular polytopes AMS Subject Classification (2000): Primary: 51M20. Secondary: 20F55.

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Barry Monson, Egon Schulte
• Keywords: Abstract Regular Polytopes, DM 2010, Polytopes, Toroidal Polytopes