Hyperbolic triangular prisms with one ideal vertex

Grant S. Lakeland; Corinne G. Roth

doi:10.2140/involve.2020.13.361

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arXiv · 1808.07904

Hyperbolic triangular prisms with one ideal vertex

Grant S. Lakeland·Corinne G. Roth

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Abstract

In this paper, we classify all of the five-sided three-dimensional hyperbolic polyhedra with one ideal vertex, which have the shape of a triangular prism. We show how to find each such polyhedron in the upper half-space model by considering lines and circles in the plane. Finally, we give matrix generators in $\mathrm{PSL}_2(\mathbb C)$ for the orientation-preserving subgroup of each corresponding reflection group.

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Grant S. Lakeland, Corinne G. Roth. 2018-08-23. Hyperbolic triangular prisms with one ideal vertex. https://doi.org/10.2140/involve.2020.13.361

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