On an elementary proof of Rivin's characterization of convex ideal hyperbolic polyhedra by their dihedral angles

DOI10.1007/s10711-004-3180-yzbMath1065.52008OpenAlexW2064620328MaRDI QIDQ1768254

Francçois Guéritaud

Publication date: 15 March 2005

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-004-3180-y

zbMATH Keywords

tessellation1-skeletoncombinatorial equivalenceBeltrami-Klein modeldual tessellationhyperbolic (ideal) polyhedraLobachevski volume function

Mathematics Subject Classification ID

Three-dimensional polytopes (52B10) Spherical and hyperbolic convexity (52A55) Elementary problems in hyperbolic and elliptic geometries (51M09)

Related Items (4)

Andreev's theorem on hyperbolic polyhedra ⋮ QUANTUM TEICHMÜLLER THEORY AND REPRESENTATIONS OF THE PURE BRAID GROUP ⋮ Canonical triangulations of Dehn fillings ⋮ On the growth rate of ideal Coxeter groups in hyperbolic 3-space.

Cites Work

• A characterization of compact convex polyhedra in hyperbolic 3-space
• Euclidean structures on simplicial surfaces and hyperbolic volume
• Combinatorial optimization in geometry
• A characterization of ideal polyhedra in hyperbolic 3-space
• On geometry of convex ideal polyhedra in hyperbolic 3-space

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