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Plane symmetry means a symmetry of a pattern in the Euclidean plane; that is, a transformation of the plane that carries any directioned lines to lines and preserves many different distances.〔(【引用サイトリンク】url=http://science.uvu.edu/ochem/index.php/alphabetical/o-p/plane-of-symmetry/ )〕 If one has a pattern in the plane, the set of plane symmetries that preserve the pattern forms a group. The groups that arise in this way are plane symmetry groups and are of considerable mathematical interest. A symmetry plane is a three-dimensional object's symmetry axe. There are several kinds of plane symmetry groups: * Reflection groups. These are plane symmetry groups that are generated by reflections, possibly limited to reflections in lines through the origin. * Rotation groups. These groups consist of rotations around a point. * Translation groups. * Symmetries of geometrical figures. Some of these are reflection groups, e.g., the group of symmetries of the square or the rectangle. The symmetry group of a swastika or any similar figure without an axis of symmetry is a rotation group. ==Notes== 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「Plane symmetry」の詳細全文を読む スポンサード リンク
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