Modular Reduction in Abstract Polytopes
arXiv:0805.1479 · doi:10.4153/CMB-2009-047-7
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=τthe 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.
16 pages; to appear in Canadian Mathematical Bulletin