Journal article

A characterization of compact convex polyhedra in hyperbolic 3-space

CD Hodgson, I Rivin

Inventiones Mathematicae | Published : 1993


In this paper we study the extrinsic geometry of convex polyhedral surfaces in three-dimensional hyperbolic space H3. We obtain a number of new uniqueness results, and also obtain a characterization of the shapes of convex polyhedra in H3 in terms of a generalized Gauss map. This characterization greatly generalizes Andre'ev's Theorem. © 1993 Springer-Verlag.

University of Melbourne Researchers

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