If you watched du Sautoy's talk on symmetry I posted yesterday and your background in Group Theory matches MS221 or M208 you might have lost him when he was talking about the symmetries found in the Alhambra. Let me explain.
These symmetry groups are called the Wallpaper Groups and they are part of the Open University Course M336 Groups and Geometry. Although there are only 17 wallpaper groups ( mathematical proof in M336 ) recognizing them in nature or in a piece of art is difficult. Well, it takes practice. This beautiful applet ( Java required on your PC ) lets you experiment with the wallpaper groups. Some theoretical background can be found here.
Enjoy!
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