Proper locally spherical hypertopes of hyperbolic type

TL;DR

This paper constructs an infinite family of locally spherical regular hypertopes of hyperbolic type based on certain hyperbolic Coxeter groups, expanding the understanding of geometric structures in hyperbolic geometry.

Contribution

It introduces a method to generate infinite locally spherical hypertopes of hyperbolic type from specific irreducible Coxeter groups with non-linear diagrams.

Findings

Constructed infinite families of hypertopes with desired properties

Extended the classification of hypertopes in hyperbolic geometry

Demonstrated the existence of such hypertopes for a broad class of Coxeter groups

Abstract

Given any irreducible Coxeter group $C$ of hyperbolic type with non-linear diagram and rank at least $4$, whose maximal parabolic subgroups are finite, we construct an infinite family of locally spherical regular hypertopes of hyperbolic type whose Coxeter diagram is the same as that of $C$.