Mathematics – Combinatorics
Scientific paper
2008-05-22
Mathematics
Combinatorics
21 pages (to appear in Discrete Mathematics)
Scientific paper
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.
Monson Barry
Schulte Egon
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