A generalized hyperbolic tetrahedra is a polyhedron (possibly non-compact) with finite volume in hyperbolic space, obtained from a tetra-hedron 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 Schläfli'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.
CITATION STYLE
Ushijima, A. (2006). A Volume Formula for Generalised Hyperbolic Tetrahedra. In Non-Euclidean Geometries (pp. 249–265). Kluwer Academic Publishers. https://doi.org/10.1007/0-387-29555-0_13
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