Abelian covers of regular hypertopes

Abstract

Known as thin residually connected incidence geometry, hypertopes extend the framework of abstract polytopes, and can be built from Coxeter groups (not necessarily with linear diagrams). A regular hypertope is a flag-transitive hypertope. In this paper, we present infinite families of regular hypertopes of ranks 5, 6 and 7, in terms of a certain group covering approach (analogous to a method proposed by Conder and the author in an earlier paper on abstract chiral polytopes, but with wider adaptation). Although the illustrative examples within these families are derived from Coxeter groups exhibiting Y-shaped diagrams, this approach is applicable to obtaining regular hypertopes from Coxeter groups with other diagrams, such that the size of the family members grows linearly with entries of their types.