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A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. There are 17 possible distinct groups. Wallpaper groups are two-dimensional symmetry groups, intermediate in complexity between the simpler frieze groups and the three-dimensional crystallographic groups (also called space groups). ==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: Image:Wallpaper_group-p4m-2.jpg| Image:Wallpaper_group-p4m-1.jpg| Image:Wallpaper_group-p4g-2.jpg| Examples A and B have the same wallpaper group; it is called p4mm in the IUC notation and *442 in the orbifold notation. Example C has a different wallpaper group, called p4mg 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Wallpaper group」の詳細全文を読む スポンサード リンク
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