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

Christopher K. Atkinson

doi:10.1007/s10711-010-9563-y

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

Christopher K. Atkinson

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 S³. 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.

Original language	English (US)
Pages (from-to)	177-211
Number of pages	35
Journal	Geometriae Dedicata
Volume	153
Issue number	1
DOIs	https://doi.org/10.1007/s10711-010-9563-y
State	Published - Aug 2011
Externally published	Yes

Keywords

Hyperbolic geometry
Polyhedron
Volume

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10.1007/s10711-010-9563-y

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AB - 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 S3. 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.

KW - Hyperbolic geometry

KW - Polyhedron

KW - Volume

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UR - https://www.scopus.com/pages/publications/79960065497#tab=citedBy

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ER -

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

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Keywords

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