2006/01/20 by Barry Monson, Monson, Barry, Egon Schulte +1
Computer Science · Mathematics · #20F55 #51M20 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Metric Geometry (math.MG) #math.CO #math.GR #math.MG #msc:20F55 #msc:51M20 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0601502
30 pages (Advances in Applied Mathematics, to appear)
arxiv created 2006/01/20 · openalex publication_date 2006/01/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When the standard representation of a crystallographic Coxeter group Γ is reduced modulo an odd prime p, a finite representation in some orthogonal space over ℤp is obtained. If Γ has a string diagram, the latter group will often be the automorphism group of a finite regular polytope. In Part I we described the basics of this construction and enumerated the polytopes associated with the groups of rank 3 and the groups of spherical or Euclidean type. In this paper, we investigate such families of polytopes for more general choices of Γ, including all groups of rank 4. In particular, we study in depth the interplay between their geometric properties and the algebraic structure of the corresponding finite orthogonal group.