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- W2149205231 abstract "We describe a characterization of convex polyhedra in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H cubed> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>H</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{H^3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E cubed> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>E</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>{E^3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> all of whose vertices lie on the unit sphere. That resolves a problem posed by Jakob Steiner in 1832." @default.
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- W2149205231 date "1992-01-01" @default.
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- W2149205231 title "A characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere" @default.
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- W2149205231 doi "https://doi.org/10.1090/s0273-0979-1992-00303-8" @default.
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