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1 results

  • 16 - A Family of 4-Polytopes

  • from IV - Miscellaneous Polytopes
  • Peter McMullen, University College London
  • Book:
    Geometric Regular Polytopes
    Published online:
    30 January 2020
    Print publication:
    20 February 2020, pp 530-545

  • Summary

    This chapter is devoted to a family of abstract regular 4-polytopes, which display remarkable parallels with the 4-dimensional pentagonal polytopes of Chapter 7. Two basic members of the family are quotients of 4-dimensional regular hyperbolic honeycombs. Their common automorphism group, of order 8160, is an extension by an involutory outer automorphism of a simple group. Part of the discussion centres on a certain regular polyhedron, which is closely related to the facet of the sole regular polytope of rank 4 dealt with in Chapter 13 whose symmetry group consists entirely of rotations. The treatment makes substantial use of a permutation representation of the automorphism group.