N. V. Abrosimov, E. S. Kudina, A. D. Mednykh, “Volumes of hyperbolic hexahedra with <nobr>$\overline{3}$</nobr>-symmetry”, Sib. Èlektron. Mat. Izv., 2016, Volume 13,Pages <nobr>1150

This article is cited in 2 papers

Geometry and topology

Volumes of hyperbolic hexahedra with $\overline{3}$-symmetry

N. V. Abrosimov^ab, E. S. Kudina^c, A. D. Mednykh^ab

^a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova str., 2, 630090, Novosibirsk, Russia
^c Gorno-Altaisk State University, Socialisticheskaya str., 34, 649000, Gorno-Altaisk, Russia

Abstract: We consider hyperbolic hexahedra with $\overline{3}$-symmetry. For these hexahedra, we find existence conditions, establish relations between the edge lengths and dihedral angles, and obtain exact formulas for the volumes.

Keywords: hyperbolic hexahedron, $\overline{3}$-symmetry, hyperbolic volume.

UDC: 514.132

MSC: 52B15, 51M20, 51M25, 51M10

Received December 4, 2016, published December 8, 2016

DOI: 10.17377/semi.2016.13.090