A volume formula for hyperbolic tetrahedra in terms of edge lengths

Jun Murakami, Akira Ushijima

    Research output: Contribution to journalArticle

    17 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)153-163
    Number of pages11
    JournalJournal of Geometry
    Issue number1-2
    Publication statusPublished - 2005 Dec



    • Hyperbolic tetrahedron
    • Quantum 6j-symbol
    • Volume formula

    ASJC Scopus subject areas

    • Geometry and Topology

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