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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2022, Volume 19, Issue 2, Pages 949–958
DOI: https://doi.org/10.33048/semi.2022.19.079 (Mi semr1552) 		 
Geometry and topology

The volume of a hyperbolic antipodal octahedron

B. Vuong

Regional Scientific and Educational Mathematical Center, Tomsk State University, pr. Lenina, 36, 634050, Tomsk, Russia
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DOI: https://doi.org/10.33048/semi.2022.19.079
Abstract: We consider the hyperbolic antipodal octahedron. It is an octahedron with antipodal symmetry in the hyperbolic space $\mathbb{H}^3$. We establish necessary and sufficient conditions for the existence of such an octahedron in $\mathbb{H}^3$. By dividing the octahedron into appropriate tetrahedra we obtain an explicit integral formula for the volume of the hyperbolic antipodal octahedron.
Keywords: hyperbolic octahedron, hyperbolic volume, antipodal symmetry, hyperbolic tetrahedron, integral formula.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-884
This work was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2022-884).
Received November 7, 2022, published December 10, 2022
Bibliographic databases:
Document Type: Article
UDC: 514.132
MSC: 52B15, 51M20, 51M25, 51M10
Language: English
Citation: B. Vuong, “The volume of a hyperbolic antipodal octahedron”, Sib. Èlektron. Mat. Izv., 19:2 (2022), 949–958
Citation in format AMSBIB
\Bibitem{Vuo22}
\by B.~Vuong
\paper The volume of a hyperbolic antipodal octahedron
\jour Sib. \`Elektron. Mat. Izv.
\yr 2022
\vol 19
\issue 2
\pages 949--958
\mathnet{http://mi.mathnet.ru/semr1552}
\crossref{https://doi.org/10.33048/semi.2022.19.079}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4518800}
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