Wallpaper Patterns
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Suggested reading:
- Visions of Symmetry, pg. 31-44, 77-78.
Relevant examples from Escher's work:
- Escher's sketches of Polya's 17 wallpaper patterns. Visions of Symmetry, pg. 24-26.
Wallpaper Patterns
This section is unfinished.
A wallpaper pattern is a plane figure which has more than one direction of translation symmetry. Most actual wallpaper fits the bill, because it must repeat left to right in order to hang in strips, and it must repeat vertically so that multiple strips can be cut from the same roll.
The lattice of translations.
The Seventeen Wallpaper Groups
This section is unfinished.
File:Test1.svg File:Test2.svg File:Test3.svg
Exercises
Related Sites
- Proof of the 17 wallpaper group classification by George Baloglou.
- Tilings by Dror Bar-Natan.
- The 17 wallpaper patterns in traditional Japanese art at Mathematics Museum (Japan).
- Wallpaper groups by David Joyce.
