Coxeter decompositions of hyperbolic simplices

TL;DR

This paper classifies Coxeter decompositions of hyperbolic simplices in dimensions greater than 3, contributing to the understanding of hyperbolic reflection groups and their geometric structures.

Contribution

It provides a classification of Coxeter decompositions of hyperbolic simplices in higher dimensions, advancing the geometric understanding of hyperbolic reflection groups.

Findings

Classified Coxeter decompositions in hyperbolic space >3D

Linked decompositions to hyperbolic reflection groups

Enhanced understanding of hyperbolic polyhedral symmetries

Abstract

Let X be a space of constant curvature and P be a convex polyhedron in X. A Coxeter decomposition of the polyhedron P is a decomposition of P into finitely many Coxeter polyhedra, such that any two polyhedra having a common facet are symmetric with respect to this facet. In this paper we classify Coxeter decompositions of simplices in hyperbolic space of dimension greater than 3. The problem is close to the classification of the finite index subgroups in the discrete hyperbolic reflection groups.