Introduction
Wallpaper groups categorize patterns by their symmetries. Subtle differences may place similar patterns in different groups, while patterns that are very different in style, color, scale or orientation may belong to the same group.
Consider the following examples:
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Example A: Cloth, Tahiti -
Example B: Ornamental painting, Nineveh, Assyria -
Example C: Painted porcelain, China
Examples A and B have the same wallpaper group; it is called p4m in the IUC notation and *442 in the orbifold notation. Example C has a different wallpaper group, called p4g or 4*2 . The fact that A and B have the same wallpaper group means that they have the same symmetries, regardless of details of the designs, whereas C has a different set of symmetries despite any superficial similarities.
A complete list of all seventeen possible wallpaper groups can be found below.
Read more about this topic: Wallpaper Group
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