Wallpaper Group - Guide To Recognising Wallpaper Groups

Guide To Recognising Wallpaper Groups

To work out which wallpaper group corresponds to a given design, one may use the following table.

Size of smallest
rotation
Has reflection?
Yes No
360° / 6 p6m p6
360° / 4 Has mirrors at 45°? p4
Yes: p4m No: p4g
360° / 3 Has rot. centre off mirrors? p3
Yes: p31m No: p3m1
360° / 2 Has perpendicular reflections? Has glide reflection?
Yes No
Has rot. centre off mirrors? pmg Yes: pgg No: p2
Yes: cmm No: pmm
none Has glide axis off mirrors? Has glide reflection?
Yes: cm No: pm Yes: pg No: p1

See also this overview with diagrams.

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