Wikipedia:Reference desk/Archives/Mathematics/2018 February 3

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February 3

Naming the wallpaper groups

We know that there are 7 possible frieze groups; T, TR, TV, TG, THG, TRVG, and TRHVG. Although there are 16 defined frieze groups, only 7 are possible. There is no such pattern as TH because any T+H will automatically have a G.

Using initials, how can we name the wallpaper groups?? If possible, please include an example of a wallpaper group that is not possible despite being defined using the rules the same way TH is done above. Georgia guy (talk) 21:21, 3 February 2018 (UTC)

Courtesy links: Wallpaper group, Frieze group. -- ToE 00:16, 4 February 2018 (UTC)

I think the table in Wallpaper group#Guide to recognizing wallpaper groups could be used for such a scheme. But seeing as there are already three naming schemes listed on the page already, all of which already try to incorporate the group structure into the names to some extent, it seems to me that another set of names isn't really needed. Keep in mind as well that the added dimension in wallpaper groups makes things more complicated. For example you can't just say R for rotation since now you have to specify the angle of rotation, and if you have two reflections you now need to specify the angle between them. --RDBury (talk) 08:03, 6 February 2018 (UTC)