Start with a single shape. Repeat it in some way―translation, reflection over a line, rotation around a point―and you have created symmetry.
Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments.
This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.
Author(s): John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss
Edition: 1
Publisher: A K Peters
Year: 2008
Language: English
Pages: 448
Front Cover
Contents
Preface
Figure Acknowledgments
Part I: Symmetries of Finite Objects and Plane Repeating Patterns
Chapter 1: Symmetries
Chapter 2: Planar Patterns
Chapter 3: The Magic Theorem
Chapter 4: The Spherical Patterns
Chapter 5: The Seven Types of Frieze Patterns
Chapter 6: Why the Magic TheoremsWork
Chapter 7: Euler’s Map Theorem
Chapter 8: Classification of Surfaces
Chapter 9: Orbifolds
Part II: Color Symmetry, Group Theory, and Tilings
Chapter 10: Presenting Presentations
Chapter 11: Twofold Colorations
Chapter 12: Threefold Colorings of Plane Patterns
Chapter 13: Other Primefold Colorings
Chapter 14: Searching for Relations
Chapter 15: Types of Tilings
Chapter 16: Abstract Groups
Part III: Repeating Patterns in Other Spaces
Chapter 17: Introducing Hyperbolic Groups
Chapter 18: More on Hyperbolic Groups
Chapter 19: Archimedean Tilings
Chapter 20: Generalized Schl¨afli Symbols
Chapter 21: Naming Archimedean and Catalan Polyhedra and Tilings
Chapter 22: The 35 “Prime” Space Groups
Chapter 23: Objects with Prime Symmetry
Chapter 24: Flat Universes
Chapter 25: The 184 Composite Space Groups
Chapter 26: Higher Still
Appendix A: Other Notations for the Plane and Spherical Groups
Bibliography
Back Cover
