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Hyperbolic Tessellating Pentahedra

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Visit this site: http://www.krickl.de/bernhard/diplom/
Author:Bernhard Krickl
Description: Krickl's diploma thesis: a list of all pentahedra that tessellate hyperbolic 3-space in the sense that they are a fundamental domain to their discrete reflection group. The list includes the volumes of those pentahedra (i.e. finitely many of them, which means nearly none), and some hints on arithmeticity of the discrete reflection groups of pyramids. With additional remarks on tessellations by hexahedra. Contents include: What are polyhedra? What are tessellations? All kinds of pentahedra; All kinds of hexahedra. Includes a list of related links.
Levels: High School (9-12), College
Languages: English
Math Topics: Polyhedra, Hyperbolic Geometry, Symmetry/Tessellations

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