  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.
