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A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere
Author(s):
Craig D.
Hodgson;
Igor
Rivin;
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:
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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Additional Information:
DOI:
10.1090/S0273-0979-1992-00303-8
PII:
S 0273-0979(1992)00303-8
Copyright of article:
Copyright
1992,
American Mathematical Society
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