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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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    For the non-euclidean case, you want to look up "Non-Euclidean Tessellations and their Groups" by W. Magnus. I cannot find anything in this book which deals with the Euclidean case though...2012-06-22
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    According to wikipedia: A proof that there were only 17 possible patterns was first carried out by Evgraf Fedorov in 1891[1] and then derived independently by George Pólya in 1924.[2][3]. [1] E. Fedorov (1891) "Simmetrija na ploskosti" [Symmetry in the plane], [Proceedings of the Imperial St. Petersburg Mineralogical Society], series 2, vol. 28, pages 345-291 (in Russian). [2] George Pólya (1924) "Über die Analogie der Kristallsymmetrie in der Ebene," Zeitschrift für Kristallographie, vol. 60, pages 278–282. [3] Weyl, Hermann (1952), Symmetry, Princeton University Press, ISBN 0-691-02374-32012-06-22
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    A search on Polya and several terms including Wallpaper does not return any hits in OU Library Services. - That is my problem. - Thanks. Just read your update.2012-06-22
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    What was the query that you used to find this ? Which database have you used ? @TomCooney2012-06-22
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    I took this information directly from the wikipedia page: http://en.wikipedia.org/wiki/Wallpaper_group . If you are using a library catalogue to search, then I would search for the names of the journals rather than the authors. Also, from the above, it seems that wallpaper group is a more modern term. Polya's article's title seems to be "On the analogue of crystal symmetry in the plane". Weyl's book is probably going to be the most accessible of the above references.2012-06-22
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    Yes, I am after that book right now. Thank you very much. - Although I am somewhat uncomfortable with having to use Wikipedia as a reference. But that's another issue.2012-06-22
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    Ok. I have the book now. Weyl refers to Polya and the paper you mentioned. It's about the same as in the M336 books I have. - I am puzzled. Maybe later in another question.2012-06-22
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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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    Thank you fretty, I have done my Google search, actually read that page and actually found this page with a 'proof'. http://www.oswego.edu/~baloglou/103/seventeen.html - I am not so good in finding original papers although I have access to the Open University Library Services. - I am looking for a published article containing the proof.2012-06-22
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    There is a good book by Conway on this stuff called "The Symmetries of Things". I have leafed through it a few times and it looks like a very interesting book (lots of beautiful colour diagrams etc). I am not sure whether he proves the theorem but there is certainly a lot of in depth discussion.2012-06-22
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    fretty see comments to question. I have several books on Symmetry, etc. that's not it.2012-06-22
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    This book is only about what you are studying...it is a book about wallpaper patterns and how the proof goes, I just do not know if it is entirely rigorous since I haven't read the book myself.2012-06-22
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    I usually accept all answers and vote them up. But that doesn't include refs to Wikipedia in the interest of the overall quality of the site. Google even downgrades websites with refs to Wikipedia. - Sorry.2012-06-22
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    I don't care about votes etc, I come on this site to give/receive answers and to share knowledge! I am not suggesting that you reference wikipedia, I merely pointed out that the article is quite good for this topic...and the fact that this is FACTUAL maths means that the quality of the page can be checked by yourself using your own knowledge. There can be no ambiguity with things that are correct. What I then remembered was the good book that I have just told you about. I will put this in with my original answer.2012-06-22
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    @fretty: Perhaps your answer would have been better as a comment?2012-06-22
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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.