# Wallpaper Groups

### Symmetry group 7 (pmg)

This group has both reflections (with parallel axes) and half-turns. The fixed points of the half-turns do not lie on the axes of reflection. The lattice is rectangular, and a quarter-rectangle of a fundamental region for the translation group is a fundamental region for the symmetry group.

On the left you see the image marked up with red lines for the axes of reflections, green lines for the axes of glide reflections, and black dots for the fixed points of the half-turns. We'll continue to use these conventions for the remaining images. Although the previous symmetry group also had reflections and half-turns, you can see the differences in the placement of the axes and fixed points.

Up to the 17 wallpaper groups

Back to the previous wallpaper group

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/