#### Vol. 13, No. 3, 2020

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Hyperbolic triangular prisms with one ideal vertex

### Grant S. Lakeland and Corinne G. Roth

Vol. 13 (2020), No. 3, 361–379
##### Abstract

We classify all of the five-sided three-dimensional hyperbolic polyhedra with one ideal vertex, which have the shape of a triangular prism, and which give rise to a discrete reflection group. 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 ${PSL}_{2}\left(ℂ\right)$ for the orientation-preserving subgroup of each corresponding reflection group.

##### Keywords
hyperbolic reflection group, prism, ideal polyhedron
Primary: 57R18
Secondary: 20F55