Abstract
In this chapter, we study the geometry of discrete groups of isometries of Sn, En, and Hn. The chapter begins with an introduction to the projective disk model of hyperbolic n-space. Convex sets and convex polyhedra in Sn, En, and Hn are studied in Sections 6.2 through 6.5. The basic properties of fundamental domains for a discrete group are examined in Sections 6.6 and 6.7. The chapter ends with a study of the basic properties of tessellations of Sn, En, and Hn.
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© 2006 Springer Science+Business Media, LLC
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(2006). Geometry of Discrete Groups. In: Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-0-387-47322-2_6
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DOI: https://doi.org/10.1007/978-0-387-47322-2_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-33197-3
Online ISBN: 978-0-387-47322-2
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