2003/09/12 by Akira Ushijima, Ushijima, Akira
Computer Science · Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Computational Geometry and Mesh Generation #Mathematics and Applications #math.GT #math.MG #msc:51M09 #msc:52A38
paper · pdf · doi:10.48550/arxiv.math/0309216
18 pages, 4 figures, minor errors corrected and two references are added. To appear in "Non-Euclidean Geometries, Ja'nos Bolyai memorial volume ...", by Kluwer Academic Press
arxiv created 2003/10/30 · arxiv updated 2009/12/01
A generalized hyperbolic tetrahedra is a polyhedron (possibly non-compact) with finite volume in hyperbolic space, obtained from a tetrahedron by the polar truncation at the vertices lying outside the space. In this paper it is proved that a volume formula for ordinary hyperbolic tetrahedra devised by J. Murakami and M. Yano can be applied to such ones. There are two key tools for the proof; one is so-called Schlafli's differential formula for hyperbolic polyhedra, and the other is a necessary and sufficient condition for given numbers to be the dihedral angles of a generalized hyperbolic simplex with respect to their dihedral angles.