Volume estimates for equiangular hyperbolic Coxeter polyhedra

TL;DR

This paper provides volume estimates for equiangular hyperbolic Coxeter polyhedra, which are hyperbolic polyhedra with equal dihedral angles, extending understanding of their geometric properties.

Contribution

It offers new volume bounds for all equiangular hyperbolic Coxeter polyhedra, including cases with ideal vertices and right-angled configurations.

Findings

Volume estimates for all equiangular hyperbolic Coxeter polyhedra

Characterization of polyhedra with dihedral angles of c0/n

Extension of volume bounds to ideal and right-angled cases

Abstract

An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to \pi/n for some fixed integer n at least 2. It is a consequence of Andreev's theorem that either n=3 and the polyhedron has all ideal vertices or that n=2. Volume estimates are given for all equiangular hyperbolic Coxeter polyhedra.