Abstract
We obtain formulas for the volume of a spherical tetrahedron with ℤ2-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.
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Original Russian Text Copyright © 2011 Kolpakov A. A., Mednykh A. D., and Pashkevich M. G.
The authors were supported by the Russian Foundation for Basic Research (Grants 09-01-00255 and 10-01-00642) and the Program “Development of the Scientific Potential of Higher School” of the Russian Federal Agency for Education (Grant 2.1.1/3707).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 3, pp. 582–600, May–June, 2011.
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Kolpakov, A.A., Mednykh, A.D. & Pashkevich, M.G. A volume formula for ℤ2-symmetric spherical tetrahedra. Sib Math J 52, 456–470 (2011). https://doi.org/10.1134/S0037446611030086
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DOI: https://doi.org/10.1134/S0037446611030086