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

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 PSL2() for the orientation-preserving subgroup of each corresponding reflection group.

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hyperbolic reflection group, prism, ideal polyhedron
Mathematical Subject Classification 2010
Primary: 57R18
Secondary: 20F55
Received: 3 October 2018
Revised: 15 December 2019
Accepted: 23 March 2020
Published: 14 July 2020

Communicated by Kenneth S. Berenhaut
Grant S. Lakeland
Department of Mathematics and Computer Science
Eastern Illinois University
Charleston, IL
United States
Corinne G. Roth
Department of Mathematics and Computer Science
Eastern Illinois University
Charleston, IL
United States