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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