, Volume 111, Issue 1, pp 77-111

A characterization of compact convex polyhedra in hyperbolic 3-space

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Summary

In this paper we study the extrinsic geometry of convex polyhedral surfaces in three-dimensional hyperbolic spaceH 3. We obtain a number of new uniqueness results, and also obtain a characterization of the shapes of convex polyhedra inH 3 in terms of a generalized Gauss map. This characterization greatly generalizes Andre'ev's Theorem.

Oblatum 12-XI-1991 & 29-V-1992