On the Characterization of Polyhedra in Hyperbolic 3-Space
Metric Geometry
2010-06-24 v1 Geometric Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1006.4445,
title = {On the Characterization of Polyhedra in Hyperbolic 3-Space},
author = {Javier Virto},
journal= {arXiv preprint arXiv:1006.4445},
year = {2010}
}
Comments
31 pages, 11 figures