Locally toroidal polytopes and modular linear groups

When the standard representation of a crystallographic Coxeter group GG (with string diagram) is reduced modulo the integer d≥2d≥2, one obtains a finite group GdGd which is often the automorphism group of an abstract regular polytope. Building on earlier work in the case that dd is an odd prime, here we develop methods to handle composite moduli and completely describe the corresponding modular polytopes when GG is of spherical or Euclidean type. Using a modular variant of the quotient criterion, we then describe the locally toroidal polytopes provided by our construction, most of which are new.