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Background: I am doing a course on Groups and Geometry ( Open University M336 ). One of the topics is the classification of the plane symmetries, a.k.a. The Wallpaper Groups.

Question: What reference contains the original proof that there exists only 17 wallpaper groups?

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    You might be interested in my translation of Pólya's 1924 article: http://www.mariuskempe.net/Writing/Pólya.pdf2015-03-05

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The wiki page contains lots of info on this. It is quite interesting.

http://en.wikipedia.org/wiki/Wallpaper_group

There is also the book by Conway, "The Symmetries of Things". I believe this has a nice discussion of how the proof works but I have never read it properly so cannot vouch for the rigour.

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    Possibly, although I thought it was a valid answer, the wiki article does explain the proof and gives references for the original papers etc.2012-06-22
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Try "The 17 Plane Symmetry Groups" by R.L.E. Schwarzenberger, The Mathematical Gazette Vol 58 No 404.