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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: We describe a characterization of convex polyhedra in $ {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}$ 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: http://dx.doi.org/10.1090/S0273-0979-1992-00303-8
Article copyright: © Copyright 1992 American Mathematical Society