A characterization of compact convex polyhedra in hyperbolic 3-space
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- Hodgson, C.D. & Rivin, I. Invent Math (1993) 111: 77. doi:10.1007/BF01231281
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In 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.