When the standard representation of a crystallographic Coxeter group G (withstring diagram) is reduced modulo the integer d>1, one obtains a finite groupG^d which is often the automorphism group of an abstract regular polytope.Building on earlier work in the case that d is an odd prime, we here developmethods to handle composite moduli and completely describe the correspondingmodular polytopes when G is of spherical or Euclidean type. Using a modularvariant of the quotient criterion, we then describe the locally toroidalpolytopes provided by our construction, most of which are new.
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