Abstract
In this chapter, we study the geometry of discrete groups of isometries of S n, E n, and H n. The chapter begins with an introduction to the projective disk model of hyperbolic n-space. Convex sets, polyhedra, and polytopes in S n, E n, and H n are studied in Sections 6.2, 6.3, and 6.4, respectively. The basic properties of fundamental domains for a discrete group are examined in Sections 6.5 and 6.6. The chapter ends with a study of the basic properties of tessellations of S n, E n, and H n.
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© 1994 Springer Science+Business Media New York
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Ratcliffe, J.G. (1994). Geometry of Discrete Groups. In: Foundations of Hyperbolic Manifolds. Graduate Texts in Mathematics, vol 149. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4013-4_6
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DOI: https://doi.org/10.1007/978-1-4757-4013-4_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94348-0
Online ISBN: 978-1-4757-4013-4
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