N. V. Abrosimov, G. A. Baigonakova, “Hyperbolic octahedron with <nobr>$mmm$</nobr>-symmetry”, Sib. Èlektron. Mat. Izv., 2013, Volume 10,Pages <nobr>123

This article is cited in 7 papers

Geometry and topology

Hyperbolic octahedron with $mmm$-symmetry

N. V. Abrosimov^ab, G. A. Baigonakova^c

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University
^c Gorno-Altaisk State University

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.

UDC: 514.132

MSC: 52B15, 51M20, 51M25, 51M09

Received December 28, 2012, published February 21, 2013