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On Application of Contemporary Proof of the Sforza Formula to Computation of Volumes of Hyperbolic Tetrahedra of Special Kind

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Abstract

In this paper, we use the contemporary proof (by Abrosimov and Mednykh) of the Sforza formula for volume of an arbitrary non-Euclidean tetrahedron to derive new formulas that express volumes of hyperbolic tetrahedra of special kind (orthoschemes and tetrahedra with the symmetry group S4) via dihedral angles.

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), Moscow, Russia

    V. A. Krasnov

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  1. V. A. Krasnov
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Correspondence to V. A. Krasnov.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 65, No. 4, Proceedings of the S. M. Nikolskii Mathematical Institute of RUDN University, 2019.

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Krasnov, V.A. On Application of Contemporary Proof of the Sforza Formula to Computation of Volumes of Hyperbolic Tetrahedra of Special Kind. J Math Sci 265, 791–802 (2022). https://doi.org/10.1007/s10958-022-06085-3

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