Wallpaper Groups

Symmetry group 14 (p31m)

This group contains reflections (whose axes are inclined at 60° to one another) and rotations of order 3. Some of the centers of rotation lie on the reflection axes, and some do not. The lattice is hexagonal. A fundamental region for the symmetry group is one-sixth of an equilateral triangle for the lattice.

There are glide reflections in this group as well. The axes of the glide reflections are midway between parallel reflection axes, so they miss the centers of all the rotations. They go in all three directions just as the reflections axes do.

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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/