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

Alexander Kolpakov (1) , Alexander Mednykh (2, 3) , Marina Pashkevich (2)

1 Département de Mathématiques [Fribourg]
2 Département de Mathématiques et Mécanique - Université d'État de Novossibirsk
3 Sobolev Institute of Mathematics

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 $\pi$ in the middle points of a certain pair of its skew edges.

Mots clés: tetrahedron; spherical geometry; volume

Domaines: Géométrie métrique [math.MG]

Alexander Kolpakov, Alexander Mednykh, Marina Pashkevich. Volume formula for a $\mathbb{Z}_2$-symmetric spherical tetrahedron through its edge lengths. Arkiv för Matematik, 2011, pp.Online first. ⟨10.1007/s11512-011-0148-2⟩. ⟨hal-00605572v2⟩