A characterization of compact convex polyhedra in hyperbolic 3-space

Abstract

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.