VI
TABLE O F CONTENT S
Chapter 6 . Finit e Group s 5 9
6.1 Finit e figure s
6.2 CN an d D/v , agai n
6.3 Additio n
6.4 Multiplicatio n
6.5 Rearrangement s
6.6 Permutation s
6.7 Note s
Chapter 7 . Cayle y Diagram s 7 3
7.1 Generator s
7.2 Rearrangin g basi c unit s
7.3 Stri p pattern s
7.4 Wallpattern s
Chapter 8 . Symmetr y i n th e Rea l Worl d 8 7
8.1 Analyzin g pattern s
8.2 Pattern s i n ar t an d architectur e
Bricks
Decorative floors an d wall s
The ar t o f M.C . Ecshe r
The ar t o f Willia m Morri s
Islamic ar t
African weaving s
Indian potter y
Rugs an d carpet s
Amish quilt s
8.3 Mathematica l project s
The 15-puzzle
More arithmeti c mo d N
Generators, relations , an d Cayle y diagram s
3-dimensional symmetr y
Magie squar e wallpattern s
8.4 Rando m project s
Kinship structure s
Chemistry
Tiling a wal l
Make you r ow n pattern s
Bibliography 9 9
Index 10
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