The volume of the Lambert cube in spherical space

DOI10.1134/S0001434609070219zbMath1187.52008MaRDI QIDQ736224

D. A. Derevnin, Alexander Mednykh

Publication date: 27 October 2009

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

hyperbolic spacespherical spaceSchläfli formulaLambert cubeLobachevskii function

Mathematics Subject Classification ID

Length, area, volume and convex sets (aspects of convex geometry) (52A38) Spherical and hyperbolic convexity (52A55)

Related Items (10)

Cone 3-Manifolds ⋮ On the volume of a spherical octahedron with symmetries ⋮ Volume formula for a \(\mathbb Z_2\)-symmetric spherical tetrahedron through its edge lengths ⋮ On integral expressions for volumes of hyperbolic tetrahedra ⋮ A volume formula for \(\mathbb Z_2\)-symmetric spherical tetrahedra ⋮ On the volume of a hyperbolic octahedron with \(\bar 3\)-symmetry ⋮ Spherical tetrahedra with rational volume, and spherical Pythagorean triples ⋮ On the Schlafli differential formula based on edge lengths of tetrahedron in \(H^{3}\) and \(S^{3}\) ⋮ Volumes of polyhedra in non-Euclidean spaces of constant curvature ⋮ Hyperbolic 3-manifolds with geodesic boundary: enumeration and volume calculation

Cites Work

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• On the volume of a hyberbolic and spherical tetrahedron
• Lambert cubes generating discrete reflection groups
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• A characterization of Gram matrices of polytopes
• On the volume formula for hyperbolic tetrahedra
• Hyperbolic volumes of Fibonacci manifolds
• On hyperbolic polyhedra arising as convex cores of quasi-Fuchsian punctured torus groups
• A formula for the volume of a hyperbolic tetrahedon
• Hyperbolic geometry: The first 150 years
• THE FUNCTIONS OF SCHLÄFLI AND LOBATSCHEFSKY

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