A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere
- 1 October 1992
- journal article
- Published by American Mathematical Society (AMS) in Bulletin of the American Mathematical Society
- Vol. 27 (2) , 246-251
- https://doi.org/10.1090/s0273-0979-1992-00303-8
Abstract
We describe a characterization of convex polyhedra in H 3 {H^3} in terms of their dihedral angles, developed by Rivin. We also describe some geometric and combinatorial consequences of that theory. One of these consequences is a combinatorial characterization of convex polyhedra in E 3 {E^3} all of whose vertices lie on the unit sphere. That resolves a problem posed by Jakob Steiner in 1832.Keywords
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