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2008 Organizing volumes of right-angled hyperbolic polyhedra
Taiyo Inoue
Algebr. Geom. Topol. 8(3): 1523-1565 (2008). DOI: 10.2140/agt.2008.8.1523

Abstract

This article defines a pair of combinatorial operations on the combinatorial structure of compact right-angled hyperbolic polyhedra in dimension three called decomposition and edge surgery. It is shown that these operations simplify the combinatorics of such a polyhedron, while keeping it within the class of right-angled objects, until it is a disjoint union of Löbell polyhedra, a class of polyhedra which generalizes the dodecahedron. Furthermore, these combinatorial operations are shown to have geometric realizations which are volume decreasing. This allows for an organization of the volumes of right-angled hyperbolic polyhedra and allows, in particular, the determination of the polyhedra with smallest and second smallest volumes.

Citation

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Taiyo Inoue. "Organizing volumes of right-angled hyperbolic polyhedra." Algebr. Geom. Topol. 8 (3) 1523 - 1565, 2008. https://doi.org/10.2140/agt.2008.8.1523

Information

Received: 15 August 2007; Revised: 12 March 2008; Accepted: 9 July 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1146.52005
MathSciNet: MR2443253
Digital Object Identifier: 10.2140/agt.2008.8.1523

Subjects:
Primary: 51M10, 57M50
Secondary: 52B99

Rights: Copyright © 2008 Mathematical Sciences Publishers

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