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

Alexander Kolpakov, Jun Murakami

Research output: Contribution to journalArticle

1 Citation (Scopus)

### 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 45-67 23 Tokyo Journal of Mathematics 39 1 Published - 2016 Jun 1

### Fingerprint

Prism
Triangular pyramid
Volume formula
Truncated tetrahedron
Analytic Continuation
Jacobian matrix
Line

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

In: Tokyo Journal of Mathematics, Vol. 39, No. 1, 01.06.2016, p. 45-67.

Research output: Contribution to journalArticle

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