Modular Reduction in Abstract Polytopes

TL;DR

This paper surveys modular reduction techniques in abstract polytopes and introduces new regular 4-polytopes of hyperbolic types using modular reduction with primes in Z[t], expanding the understanding of their automorphism groups.

Contribution

It provides a comprehensive survey of modular reduction in polytopes and constructs new regular 4-polytopes with automorphism groups based on finite orthogonal groups using primes in Z[t].

Findings

Survey of modular reduction literature in polytopes

Construction of new regular 4-polytopes {3,5,3} and {5,3,5}

Automorphism groups given by finite orthogonal groups

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=\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.