# Wallpaper Groups

### Symmetry group 17 (p6m)

This most complicated group has rotations of order 2, 3, and 6 as well as
reflections. The axes of reflection meet at all the centers of rotation. At
the centers of the order-6 rotations, six reflection axes meet and are
inclined at 30° to one another. The lattice is hexagonal. A fundamental region for the symmetry group is one-twelfth of an equilateral triangle for the lattice.

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, so they pass through the centers of the half-turns (black dots). They go in all six directions just as the reflections axes do.

Up to the 17 wallpaper groups

Back to the previous 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/