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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2013, Volume 10, Pages 123–140 (Mi semr403)  
This article is cited in 7 scientific papers (total in 7 papers)

Geometry and topology

Hyperbolic octahedron with $mmm$-symmetry

N. V. Abrosimovab, G. A. Baigonakovac

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
c Gorno-Altaisk State University
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Abstract: We consider hyperbolic octahedra with $mmm$-symmetry. We provide an existence theorem for them and establish trigonometrical identities involving lengths of edges and dihedral angles (the sine-tangent rules). Then we apply the Schläfli formula to find the volume of prescribed octahedra in terms of dihedral angles explicitly.
Keywords: hyperbolic octahedron, mmm-symmetry, hyperbolic volume, existence theorem, sine-tangent rule.
Received December 28, 2012, published February 21, 2013
Document Type: Article
UDC: 514.132
MSC: 52B15, 51M20, 51M25, 51M09
Language: Russian
Citation: N. V. Abrosimov, G. A. Baigonakova, “Hyperbolic octahedron with $mmm$-symmetry”, Sib. Èlektron. Mat. Izv., 10 (2013), 123–140
Citation in format AMSBIB
\Bibitem{AbrBai13}
\by N.~V.~Abrosimov, G.~A.~Baigonakova
\paper Hyperbolic octahedron with $mmm$-symmetry
\jour Sib. \`Elektron. Mat. Izv.
\yr 2013
\vol 10
\pages 123--140
\mathnet{http://mi.mathnet.ru/semr403}
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