Volume of a doubly truncated hyperbolic tetrahedron

Alexander Kolpakov (1) , Jun Murakami (2)

1 Département de Mathématiques [Fribourg]
2 Departement of Mathematics [Waseda]

The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the previous results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different geometric cases via dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.

Mots clés: hyperbolic tetrahedron; Gram matrix; volume formula

Domaines: Géométrie métrique [math.MG]

Alexander Kolpakov, Jun Murakami. Volume of a doubly truncated hyperbolic tetrahedron. Aequationes Mathematicae, 2012, 85 (3), pp.449-463. ⟨10.1007/s00010-012-0153-y⟩. ⟨hal-00713381v6⟩