Itajime Shibori Wallpapers

Date started: May 2017
Leads: Carolyn Yackel

Abstract

The goal of this project was to use global shibori techniques, such as folding and clamping, to create all seventeen wallpaper patterns.  However, by appealing to the language of oribfolds it becomes clear that only the seven such patterns not involving rotations and with orbifolds achievable in our three-dimensional world can be made.  These are o/p1, **/pm, *x/cm, *632/p6m, *442/p4m, *332/p3m1, and *2222/pmm, where the slash denotes equivalence of notations rather than a two-color symmetry.

Media

*333 or p3m1
*442 or p4m
*x or cm

References

  • Conway, Burgiel, and Goodman-Strauss.  {\sl The Symmetries of Things}. Wellesley, MA: AK Peters, 2008.
  • Vihart. “Snowflakes, Starflakes, and Swirlflakes”.  Youtube video, 4:03. Posted [December 2012]. https://www.youtube.com/watch?v=8EmhGOQ-DNQ.