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A volume formula for hyperbolic tetrahedra in terms of edge lengths

Jun Murakami·Akira Ushijima
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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.

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Jun Murakami, Akira Ushijima. 2004-02-05. A volume formula for hyperbolic tetrahedra in terms of edge lengths. https://arxiv.org/abs/math/0402087

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