Chiral polytopes and Suzuki simple groups

Abstract

For each q ≠ 2 an odd power of 2, we show that the Suzuki simple group S D Sz(q) is the automorphism group of considerably more chiral polyhedra than regular polyhedra. Furthermore, we show that S cannot be the automorphism group of an abstract chiral polytope of rank greater than 4. For each almost simple group G such that S < G ≤ Aut(S), we prove that G is not the automorphism group of an abstract chiral polytope of rank greater than 3, and produce examples of chiral 3-polytopes for each such group G.