Volume 9, issue 2 (2009)

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Volume estimates for equiangular hyperbolic Coxeter polyhedra

Christopher K Atkinson

Algebraic & Geometric Topology 9 (2009) 1225–1254
Abstract

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

Keywords
hyperbolic geometry, Coxeter polyhedra, $3$-orbifolds
Primary: 57M50
Secondary: 30F40