Volume formula for a $\mathbb{Z}_2$ -symmetric spherical tetrahedron through its edge lengths

preprint2011arXivOpen access

The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation through angle $π$ in the middle points of a certain pair of its skew edges.

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Volume formula for a $\mathbb{Z}_2$ -symmetric spherical tetrahedron through its edge lengths

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Volume formula for a Z2\mathbb{Z}_2Z2​-symmetric spherical tetrahedron through its edge lengths

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Volume formula for a $\mathbb{Z}_2$ -symmetric spherical tetrahedron through its edge lengths