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arXiv · 1409.3355

The dual Jacobian of a generalised tetrahedron, and volumes of prisms

Alexander Kolpakov·Jun Murakami
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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 Schl\"afli formula.

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Alexander Kolpakov, Jun Murakami. 2014-09-11. The dual Jacobian of a generalised tetrahedron, and volumes of prisms. https://arxiv.org/abs/1409.3355

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