Algebraic & Geometric Topology

Volume estimates for equiangular hyperbolic Coxeter polyhedra

Christopher K Atkinson

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An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to πn for some fixed n, n2. 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

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

Received: 26 June 2008
Revised: 6 May 2009
Accepted: 11 May 2009
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 30F40: Kleinian groups [See also 20H10]

hyperbolic geometry Coxeter polyhedra $3$-orbifolds


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.

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