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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.

  1. 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 tex2html_wrap_inline13 (i.e., by one-third of tex2html_wrap_inline15 ), but by no smaller angle.
  2. 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.
  3. Finally, use the flow-chart to classify each of the 11 plane patterns that you constructed and drew from the planar clusters.

Carl Lee
Wed Nov 4 12:32:39 EST 1998