Volume of a doubly truncated hyperbolic tetrahedron

Volume of a doubly truncated hyperbolic tetrahedron

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 properl...

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Veröffentlicht in:Aequationes mathematicae 2013-06, Vol.85 (3), p.449-463
Hauptverfasser: Kolpakov, Alexander, Murakami, Jun
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Combinatorics
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Metric Geometry
Strata
Tetrahedrons
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Zusammenfassung: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.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-012-0153-y