Wallpaper Symmetry

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Wallpaper Symmetry
Presented by Morgan Marshall and Jennifer Nuckols
Tuesday, March 7, 2000 Afternoon SME
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Wallpaper Symmetry
Infinitely Periodic repetition of basic image

Vs.
No.
Yes.
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Wallpaper Symmetry
Basic Image Fundamental Region Symmetry
Operation Isometry
Four basic isometries
Reflection Glide Reflection
Translation Rotation
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Wallpaper Symmetry
There are exactly 17 different wallpaper patterns.

• Subtle mathematics involved
• Limited number of isometries and combinations
• Limited number of shapes

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Wallpaper Symmetry
Symmetry Group 1 (p1)
Isometries
Translation
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Wallpaper Symmetry
Symmetry Group 2 (p2)
Isometries
Translation Rotation
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Wallpaper Symmetry
Symmetry Group 11 (p4m)
Isometries
Reflection 2-Fold Rotation 4-Fold
Rotation Translation
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Wallpaper Symmetry
Symmetry Group 17 (p6m)
Isometries
Reflection 2-Fold Rotation 3-Fold
Rotation 6-Fold Rotation Translation
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Wallpaper Symmetry
Memorial Church
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Wallpaper Symmetry
Green Library
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Wallpaper Symmetry
All involve the infinite repetition of a
fundamental region Translate in 1
direction Border Patterns Translate in 2
directions Wallpaper Patterns Translate in 3
direction 3D Objects
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Wallpaper Symmetry
Fin