# Wallpaper Groups

### Symmetry group 1 (p1)

This is the simplest symmetry group. It consists only of translations. There are neither reflections, glide-reflections, nor rotations. The two translation axes may be inclined at any angle to each other. Its lattice
is parallelogrammatic, so a fundamental region for the symmetry group is the same as that for the translation group, namely, a parallelogram.

For many actual wallpaper patterns, translations are the only trasformations that leave the pattern invariant. One of the translation directions is vertical, up and down the wallpaper strip. Usually, horizontal transations are not invariant on commercial wallpaper. Instead, the pattern is raised or lowered on adjacent wallpaper strips.

Up to the 17 wallpaper groups

On to the next wallpaper group

© 1994, 1997.

David E. Joyce

Department of Mathematics and Computer Science

Clark University

Worcester, MA 01610

These files are located at http://aleph0.clarku.edu/~djoyce/wallpaper/