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Handbook of regular patterns: An introduction to symmetry in two dimensions by Peter S. Stevens (Author)

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This book explores symmetry and pattern structures across different cultures and periods. It covers a wide range of topics, including symmetry groups, frieze patterns, wallpaper groups, and the mathematical principles underlying these concepts. The book is well-illustrated and includes many examples and exercises to help readers understand the material. Extensive coverage of historic examples of Frieze groups.

Table of Contents:

I. Symmetry Groups

  1. Basic Operations - 2
  2. How Operations Generate Themselves - 10

II. Point Groups

  1. Point Groups - 18
  2. The Asymmetric Motif: Group 1 - 22
  3. Bilateral Symmetry: Group m - 28
  4. Playing Cards and Walnuts: Groups 2 and 2mm - 38
  5. The Triskelion and the Green Pepper: Groups 3 and 3m - 52
  6. The Swastika and the Greek Cross: Groups 4 and 4mm - 58
  7. Flowers and Pentagrams: Groups 5 and 5m - 72
  8. Solomon’s Seal and Snowflakes: Groups 6 and 6mm - 80
  9. Stars and Circles: Point Groups of Higher Order - 84

III. The Seven Line Groups

  1. Ducks in a Row: Group t - 96
  2. Friday’s Footprints: Group tg - 106
  3. Reflected Reflections: Group tm - 118
  4. Reflected Sails: Group mt - 126
  5. Grand Right and Left: Group f2 - 136
  6. Reflected Whirls: Group t2mg - 148

IV. The Seventeen Plane Groups

  1. Linear Kaleidoscope: Group t2mm - 158
  2. Recapitulation - 166
  3. Two Nonparallel Translations: Group p1 - 170
  4. Two Parallel Glide Reflections: Group pg - 182
  5. Two Parallel Mirrors: Group pm - 192
  6. A Reflection and a Parallel Glide Reflection: Group cm - 198
  7. Four Half-Turns: Group p2 - 208
  8. A Mirror and a Perpendicular Glide Reflection: Group p2mg - 218
  9. Two Perpendicular Glide Reflections: Group p2gg - 230
  10. Reflections in Four Sides of a Rectangle: Group p2mm - 242
  11. Perpendicular Mirrors and Perpendicular Glide Reflections: Group c2mm - 248
  12. Three Rotations Through 120°: Group p3 - 258
  13. Reflections in an Equilateral Triangle: Group p3m1 - 264
  14. Reflections of 120° Turns: Group p31m - 272
  15. Quarter-Turns: Group p4 - 280
  16. Reflections of Quarter-Turns: Group p4gm - 290
  17. Reflections in the Sides of a 45°-45°-90° Triangle: Group p4mm - 302
  18. Sixfold Rotations: Group p6 - 314
  19. Reflections in the Sides of a 30°-60°-90° Triangle: Group p6mm - 324
  20. Summary - 332

Appendix Derivations and the Absence of Group p5 - 376

Bibliography - 392 Index - 394

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