On the Characterization of Polyhedra in Hyperbolic 3-Space

Details On the Characterization of Polyhedra in Hyperbolic 3-Space On the Characterization of Polyhedra in Hyperbolic 3-Space

2010-06-23

arxiv.org/abs/1006.4445v1

Mathematics

Metric Geometry

31 pages, 11 figures

Scientific paper

We review several results related to the characterization of polyhedra in hyperbolic 3-space. In particular we present Rivin's theorem that gives a characterization of compact convex hyperbolic polyhedra, and Hodgson's proof of the Adreev's theorem. We also review the analogous characterization of ideal polyhedra, and give a family of counter-examples that proves that hyperbolic polyhedra are not determined by edge lengths.

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