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Volume of a doubly truncated hyperbolic tetrahedron

An Erratum to this article was published on 07 January 2014


The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the earlier results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different geometric cases by dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.

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Corresponding author

Correspondence to Alexander Kolpakov.

Additional information

A. Kolpakov was supported by the Schweizerischer National fonds SNF no. 200021-131967/1.

J. Murakami was supported by Grant-in-Aid for Scientific Research no. 22540236.

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Kolpakov, A., Murakami, J. Volume of a doubly truncated hyperbolic tetrahedron. Aequat. Math. 85, 449–463 (2013).

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Mathematics Subject Classification

  • Primary 51M25
  • Secondary 51M09


  • Hyperbolic tetrahedron
  • Gram matrix
  • volume formula