Volume estimates for equiangular hyperbolic Coxeter polyhedra

Abstract

An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to $\pi ∕n$ for some fixed $n\in \mathbb{Z}$, $n\ge 2$. 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.