A characterization of compact convex polyhedra in hyperbolic 3-space

@article{Hodgson1993ACO,
  title={A characterization of compact convex polyhedra in hyperbolic 3-space},
  author={Craig Hodgson and Igor Rivin},
  journal={Inventiones mathematicae},
  year={1993},
  volume={111},
  pages={77-111}
}
SummaryIn this paper we study the extrinsic geometry of convex polyhedral surfaces in three-dimensional hyperbolic spaceH3. We obtain a number of new uniqueness results, and also obtain a characterization of the shapes of convex polyhedra inH3 in terms of a generalized Gauss map. This characterization greatly generalizes Andre'ev's Theorem. 
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