Modular Reduction in Abstract Polytopes

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Monson, B.
Schulte, Egon
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Abstract
Description
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 Z[t] (with t=\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.
Comment: 16 pages; to appear in Canadian Mathematical Bulletin
Keywords
Mathematics - Combinatorics, Mathematics - Metric Geometry, 51M20, 20F55
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