  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.
