A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere

Authors:
Craig D. Hodgson, Igor Rivin and Warren D. Smith

Journal:
Bull. Amer. Math. Soc. **27** (1992), 246-251

MSC (2000):
Primary 52B12; Secondary 51M10, 52A55, 68U05

MathSciNet review:
1149872

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Abstract | References | Similar Articles | Additional Information

Abstract: We describe a characterization of convex polyhedra in 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 all of whose vertices lie on the unit sphere. That resolves a problem posed by Jakob Steiner in 1832.

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DOI:
http://dx.doi.org/10.1090/S0273-0979-1992-00303-8

Article copyright:
© Copyright 1992
American Mathematical Society