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On the volume of a hyperbolic octahedron with \(\bar 3\)-symmetry

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Abstract

We consider hyperbolic octahedra with \(\bar 3\)-symmetry. For these octahedra, we find existence conditions, establish relations between the edge lengths and dihedral angles, and obtain exact formulas for the volumes.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, pr. Akademika Koptyuga 4, Novosibirsk, 630090, Russia

    N. V. Abrosimov & A. D. Mednykh

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    N. V. Abrosimov & A. D. Mednykh

  3. Laboratory of Quantum Topology, Chelyabinsk State University, ul. Brat’ev Kashirinykh 129, Chelyabinsk, 454001, Russia

    N. V. Abrosimov & A. D. Mednykh

  4. Gorno-Altaisk State University, ul. Lenkina 1, Gorno-Altaisk, 649000, Altai Republic, Russia

    E. S. Kudina

Authors
  1. N. V. Abrosimov
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  2. E. S. Kudina
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  3. A. D. Mednykh
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Correspondence to N. V. Abrosimov.

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Abrosimov, N.V., Kudina, E.S. & Mednykh, A.D. On the volume of a hyperbolic octahedron with \(\bar 3\)-symmetry. Proc. Steklov Inst. Math. 288, 1–9 (2015). https://doi.org/10.1134/S0081543815010010

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  • DOI: https://doi.org/10.1134/S0081543815010010

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