Regular polytopes of type {4,4,3} and {4,4,4}

Abstract

Abstract regular polytopes generalize the classical concept of a regular polytope and regular tessellation to more complicated combinatorial structures with a distinctive geometrical and topological flavour. In this paper the authors give an almost complete classification of the (universal) locally toroidal regular 4-polytopes of Schläfli types {4,4,3} and {4,4,4}.

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McMullen, P., Schulte, E. Regular polytopes of type {4,4,3} and {4,4,4}. Combinatorica 12, 203–220 (1992). https://doi.org/10.1007/BF01204723

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AMS subject classification (1991)

  • 51 M 20
  • 52 B 15