Modular Reduction in Abstract Polytopes
Abstract
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=τ 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.
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