Hypertopes with Tetrahedral Diagram

  • Domenico Catalano
  • M. Elisa Fernandes
  • Isabel Hubard
  • Dimitri Leemans
Keywords: Regularity, Chirality, Thin geometries, Hypermaps, Abstract polytopes


In this paper we construct an infinite family of hypertopes of rank four having the complete graph $K_4$ as diagram. Their group of rotational symmetries is isomorphic to $PSL(2,q)$. It turns out some elements of this family are regular hypertopes and some are chiral. Moreover, we show that the chiral ones have both improper and proper correlations simultaneously.


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