Difference between revisions of "Wallpaper Patterns"
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Revision as of 01:48, 5 February 2007
- 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.
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
Escher's Use of Symmetry
Escher's Regular Division of the Plane Drawings served as source material for his finished printed works. The vast majority of these fall into one of seven symmetry groups: p1, p2, p3, p4, p6, pg, and pgg.
- 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.