**The Great Pattern Classification Challenge
**

**
You have already heard that there are only 17 types of repeating
plane (wallpaper) patterns. Now you will be given the tools to
analyze and classify such patterns.
**

**First a definition. You already know what reflections, rotations, and glide-reflections are. The enclosed flow-chart uses the term ``threefold center.'' A rotation center is a threefold center if the pattern can be rotated about that point by (i.e., by one-third of ), but by no smaller angle.****Enclosed is a flow-chart and examples of the 17 different types of patterns. Your mission is to use the flowchart to identify each pattern correctly. Write the correct pattern identification (e.g., ``p3m1'') next to each pattern. You should have a different label for each pattern.****Finally, use the flow-chart to classify each of the 11 plane patterns that you constructed and drew from the planar clusters.**

Wed Nov 4 12:32:39 EST 1998