## Algebraic & Geometric Topology

### Volume estimates for equiangular hyperbolic Coxeter polyhedra

Christopher K Atkinson

#### Abstract

An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to $π∕n$ for some fixed $n∈ℤ$, $n≥2$. 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 9, Number 2 (2009), 1225-1254.

Dates
Revised: 6 May 2009
Accepted: 11 May 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513797013

Digital Object Identifier
doi:10.2140/agt.2009.9.1225

Mathematical Reviews number (MathSciNet)
MR2519588

Zentralblatt MATH identifier
1170.57012

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds

#### Citation

Atkinson, Christopher K. Volume estimates for equiangular hyperbolic Coxeter polyhedra. Algebr. Geom. Topol. 9 (2009), no. 2, 1225--1254. doi:10.2140/agt.2009.9.1225. https://projecteuclid.org/euclid.agt/1513797013

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