Wallpaper Groups

Symmetry group 11 (p4m)

This group differs from the last one (p4) in that it also has reflections. The axes of reflection are inclined to each other by 45° so that four axes of reflection pass through the centers of the order-4 rotations. In fact, all the rotation centers lie on the reflection axes. The lattice is square, and an eighth, a triangle, of a fundamental region for the translation group is a fundamental region for the symmetry group.

There are glide reflections in this group as well, but the image is pretty cluttered even without their axes being drawn. The axes of the glide reflections are midway between parallel reflection axes. They go in all four directions just as the reflections axes do. Some of them pass through the centers of the half-turns (black dots), but others miss those centers.

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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/