wallpaper symmetries

Arthur Lee, Jul 27, 2014

study symmetries of wallpaper patterns and related tiling

Table of Contents

  1. 17 symmetry groups
    1. p1 frame
    2. p2 frame
    3. pm frame
    4. pg frame
    5. cm frame
    6. cmm frame
    7. pmm frame
    8. pmg frame
    9. pgg frame
    10. p4 frame
    11. p4g frame
    12. p4m frame
    13. p3 frame
    14. p31m frame
    15. p3m1 frame
    16. p6 frame
    17. p6m frame
  2. special tiles
    1. generate p3 hexagon tile
    2. p3 pattern
    3. cairo from pgg
    4. pentagon tiles from p4
    5. Cairo from p4

1.

17 symmetry groups

  • 1. p1 frame
  • 2. p2 frame
  • 3. pm frame
  • 4. pg frame
  • 5. cm frame
  • 6. cmm frame
  • 7. pmm frame
  • 8. pmg frame
  • 9. pgg frame
  • 10. p4 frame
  • 11. p4g frame
  • 12. p4m frame
  • 13. p3 frame
  • 14. p31m frame
  • 15. p3m1 frame
  • 16. p6 frame
  • 17. p6m frame

1.1.

p1 frame

p1 frame
– Arthur Lee

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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1.17.

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2.

special tiles

  • 1. generate p3 hexagon tile
  • 2. p3 pattern
  • 3. cairo from pgg
  • 4. pentagon tiles from p4
  • 5. Cairo from p4

2.1.

generate p3 hexagon tile

generate p3 hexagon tile
– Arthur Lee

2.2.

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2.3.

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2.4.

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2.5.

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