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How to Find a Mirror String

For any two dimensional symmetry group, you can find and describe a mirror string (if one exists) by the following method:
  1. Start anywhere on the surface and walk in a straight line until you crash into a line of mirror symmetry.

  2. As your head hits the mirror, you'll see stars, so record this by writing "*" in your notebook.

  3. Remember what your surroundings look like.

  4. Follow the mirror along until perhaps you run into an intersecting mirror line. If this happens, you are at an "n-way kaleidoscopic point", where n (the "order" of the kaleidoscopic point) is the number of mirror lines through this point. Record the value of n in your notebook after the *, then turn right as sharply as you can.

  5. Continue in this way until you reach the first point that's identical to the point where we hit the first mirror. Your notebook will contain a symbol *abc..., where a,b,c,... are the orders of the kaleidoscopic points (if any) that you met on your walk. You have just explored a "mirror string of type *abc...".

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Author: Heidi Burgiel
Comments to: webmaster@geom.umn.edu
Created: Dec 7 1995 --- Last modified: Tue Jun 11 08:45:09 1996
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