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The Symmetries of Things
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monograph
Publication date
(Online):
April 11 2016
Publisher:
A K Peters/CRC Press
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Can One Hear the Shape of a Drum?
Mark Kac
(1966)
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Riemannian Coverings and Isospectral Manifolds
Toshikazu Sunada
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Sur les substitutions orthogonales et les divisions régulières de l'espace
Edouard Goursat
(1889)
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Book Chapter
Publication date (Print):
April 18 2008
Publication date (Online):
April 11 2016
Pages
: 419-422
DOI:
10.1201/b21368-32
SO-VID:
d32691b0-27bd-4863-9003-14531a8cec7e
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Book chapters
pp. 1
Symmetries of Finite Objects and Plane Repeating Patterns
pp. 7
Symmetries
pp. 15
Planar Patterns
pp. 29
The Magic Theorem
pp. 51
The Spherical Patterns
pp. 67
The Seven Types of Frieze Patterns
pp. 75
Why the Magic TheoremsWork
pp. 83
Euler’s Map Theorem
pp. 93
Classification of Surfaces
pp. 109
Orbifolds
pp. 117
Color Symmetry, Group Theory, and Tilings
pp. 125
Presenting Presentations
pp. 135
Twofold Colorations
pp. 153
Threefold Colorings of Plane Patterns
pp. 161
Other Primefold Colorings
pp. 171
Searching for Relations
pp. 185
Types of Tilings
pp. 199
Abstract Groups
pp. 215
Repeating Patterns in Other Spaces
pp. 219
Introducing Hyperbolic Groups
pp. 231
More on Hyperbolic Groups
pp. 251
Archimedean Tilings
pp. 269
Generalized Schl¨afli Symbols
pp. 283
Naming Archimedean and Catalan Polyhedra and Tilings
pp. 301
The 35 “Prime” Space Groups
pp. 327
Objects with Prime Symmetry
pp. 355
Flat Universes
pp. 367
The 184 Composite Space Groups
pp. 383
Higher Still
pp. 415
Other Notations for the Plane and Spherical Groups
pp. 419
Bibliography
pp. 423
Index
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