# Wallpaper Groups

### Symmetry group 6 (pmm)

This symmetry group contains reflections whose axes are perpendicular. There are no glide-reflections (except those which have the same axis as an axis of reflection). The only rotations are half-turns whose fixed points lie at intersections of axes of reflection. The lattice is rectanglular, and a rectangle can be chosen for the fundamental region of the translation group so that a quarter-rectangle of it is a fundamental region for the symmetry group.

You can see the axes of reflection in red in the image on the right. The black dots indicate the fixed points of half turns.

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© 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/