Hypertopes with Tetrahedral Diagram

Abstract

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.