### Abstract

We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of the former, that falls in line with a similar behaviour of the corresponding volume formulae. Also, we obtain a volume formula for a hyperbolic n-gonal prism: the proof requires the above mentioned Jacobian, employed in the analysis of the edge lengths behaviour of such a prism, needed later for the Schläfli formula.

Original language | English |
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Pages (from-to) | 45-67 |

Number of pages | 23 |

Journal | Tokyo Journal of Mathematics |

Volume | 39 |

Issue number | 1 |

Publication status | Published - 2016 Jun 1 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Tokyo Journal of Mathematics*,

*39*(1), 45-67.

**The dual jacobian of a generalised hyperbolic tetrahedron, and volumes of prisms.** / Kolpakov, Alexander; Murakami, Jun.

Research output: Contribution to journal › Article

*Tokyo Journal of Mathematics*, vol. 39, no. 1, pp. 45-67.

}

TY - JOUR

T1 - The dual jacobian of a generalised hyperbolic tetrahedron, and volumes of prisms

AU - Kolpakov, Alexander

AU - Murakami, Jun

PY - 2016/6/1

Y1 - 2016/6/1

N2 - We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of the former, that falls in line with a similar behaviour of the corresponding volume formulae. Also, we obtain a volume formula for a hyperbolic n-gonal prism: the proof requires the above mentioned Jacobian, employed in the analysis of the edge lengths behaviour of such a prism, needed later for the Schläfli formula.

AB - We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of the former, that falls in line with a similar behaviour of the corresponding volume formulae. Also, we obtain a volume formula for a hyperbolic n-gonal prism: the proof requires the above mentioned Jacobian, employed in the analysis of the edge lengths behaviour of such a prism, needed later for the Schläfli formula.

UR - http://www.scopus.com/inward/record.url?scp=84983627778&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983627778&partnerID=8YFLogxK

M3 - Article

VL - 39

SP - 45

EP - 67

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 1

ER -