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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere
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by Craig D. Hodgson, Igor Rivin and Warren D. Smith PDF
Bull. Amer. Math. Soc. 27 (1992), 246-251 Request permission

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
  • © Copyright 1992 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 27 (1992), 246-251
  • MSC (2000): Primary 52B12; Secondary 51M10, 52A55, 68U05
  • DOI: https://doi.org/10.1090/S0273-0979-1992-00303-8
  • MathSciNet review: 1149872