Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra
arXiv:1008.5396 · doi:10.1007/s10711-010-9563-y
Abstract
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, Schläfli's formula, and previous results of the author giving volume bounds for right-angled hyperbolic polyhedra.
36 pages, 19 figures