On the Schlafli differential formula based on edge lengths of tetrahedron in \(H^{3}\) and \(S^{3}\)

DOI10.1007/s10711-008-9301-xzbMath1168.51006OpenAlexW1995697411MaRDI QIDQ1014918

Serkan Kader, Murat Savas, Atakan T. Yakut

Publication date: 29 April 2009

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

Full work available at URL: https://doi.org/10.1007/s10711-008-9301-x

zbMATH Keywords

hyperbolic tetrahedronhypothetic and spherial spacevolume of polyhedra

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Polyhedra and polytopes; regular figures, division of spaces (51M20) Spherical and hyperbolic convexity (52A55) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Differential invariants (local theory), geometric objects (53A55) Reflection groups, reflection geometries (51F15)

Related Items (3)

Flat connections in three-manifolds and classical Chern-Simons invariant ⋮ Calculus of generalized hyperbolic tetrahedra ⋮ Explicit volume formula for a hyperbolic tetrahedron in terms of edge lengths

Cites Work

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• On a problem of Fenchel
• The volume of the Lambert cube in spherical space
• A volume formula for hyperbolic tetrahedra in terms of edge lengths
• On the volume of a hyberbolic and spherical tetrahedron
• On the volume of hyperbolic polyhedra
• A lower bound for the volume of hyperbolic 3-orbifolds
• The law of sines for tetrahedra and \(n\)-simplices
• The generalized sine theorem and inequalities for simplices
• Geometry II: spaces of constant curvature. Transl. from the Russian by V. Minachin
• A Schläfli differential formula for simplices in semi-Riemannian hyperquadrics, Gauss-Bonnet formulas for simplices in the de Sitter sphere and the dual volume of a hyperbolic simplex
• Volume of a tetrahedron in terms of dihedral angles and circumradius
• On the volume formula for hyperbolic tetrahedra
• Edge matrix of hyperbolic simplices
• Vertex angles of a simplex in hyperbolic space \(H^n\)
• ON INFINITESIMAL SYMMETRIZATION AND VOLUME FORMULA FOR SPHERICAL OR HYPERBOLIC TETRAHEDRONS

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