A. A. Kolpakov, A. D. Mednykh, M. G. Pashkevich, “A volume formula for <nobr>$\mathbb Z_2$</nobr>-symmetric spherical tetrahedra”, Sibirsk. Mat. Zh., 2011, Volume 52, Number 3,Pages <nobr>582

This article is cited in 4 papers

A volume formula for $\mathbb Z_2$-symmetric spherical tetrahedra

A. A. Kolpakov^ab, A. D. Mednykh^ab, M. G. Pashkevich^c

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk
^c Novosibirsk State University for Economics and Management, Novosibirsk

Abstract: We obtain formulas for the volume of a spherical tetrahedron with $\mathbb Z_2$-symmetry realized as rotation about the axis passing through the midpoints of a pair of skew edges. We show the dependence of the volume formula on the edge lengths and dihedral angles of the tetrahedron. Several different formulas result whose scopes are determined by the geometric characteristics of the tetrahedron.

Keywords: tetrahedron, spherical space, volume, Gram matrix.

UDC: 514.13+514.135

Received: 24.06.2010