Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra

Details Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra

2010-08-31

arxiv.org/abs/1008.5396v1

Mathematics

Geometric Topology

36 pages, 19 figures

Scientific paper

We give a method for computing upper and lower bounds for the volume of a non-obtuse hyperbolic polyhedron in terms of the combinatorics of the 1-skeleton. We introduce an algorithm that detects the geometric decomposition of good 3-orbifolds with planar singular locus and underlying manifold the 3-sphere. The volume bounds follow from techniques related to the proof of Thurston's Orbifold Theorem, Schl\"afli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.

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