Inventiones mathematicae

, Volume 111, Issue 1, pp 77–111

A characterization of compact convex polyhedra in hyperbolic 3-space

  • Craig D. Hodgson
  • Igor Rivin

DOI: 10.1007/BF01231281

Cite this article as:
Hodgson, C.D. & Rivin, I. Invent Math (1993) 111: 77. doi:10.1007/BF01231281


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.

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Craig D. Hodgson
    • 1
  • Igor Rivin
    • 2
  1. 1.Mathematics DepartmentUniversity of MelbourneParkvilleAustralia
  2. 2.NEC Research Institute and Mathematics DepartmentPrinceton UniversityPrincetonUSA