A volume formula for hyperbolic tetrahedra in terms of edge lengths

By Jun Murakami, Akira Ushijima. 2004

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Abstract.We give a closed formula for volumes of generic hyperbolic tetrahedra in terms of edge lengths. The cue of our formula is by the volume conjecture for the Turaev-Viro invariant of closed 3-manifolds, which is defined from the quantum 6j -symbols. This formula contains the dilogarithm functions, and we specify the adequate branch to get the actual value of the volumes.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1aec987199f20bd41badc65f57bcc383b28328a1