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

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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 S 3. 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.

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  1. Department of Mathematics, Temple University, Wachman Hall, 1805 North Broad Street, Philadelphia, PA, 19122, USA

    Christopher K. Atkinson

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  1. Christopher K. Atkinson
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Atkinson, C.K. Two-sided combinatorial volume bounds for non-obtuse hyperbolic polyhedra. Geom Dedicata 153, 177–211 (2011). https://doi.org/10.1007/s10711-010-9563-y

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