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

Craig D. Hodgson·Igor Rivin·Warren D. Smith
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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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Craig D. Hodgson, Igor Rivin, Warren D. Smith. 1992-10-01. A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere. https://arxiv.org/abs/math/9210218

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