![]() The “x-axis” of the cell is the left edge of the cell (the vector directed downward). In two cases a “centered cell” is chosen so that reflection axes will be normal to one or both sides of the cell. Usually a “primitive cell” (a lattice unit) is chosen with centers of highest order of rotation at the vertices. The crystallographic notation consists of four symbols which identify the conventionally chosen “cell,” the highest order of rotation, and other fundamental symmetries. (The Plane Symmetry Groups: Their recognition and notation. (The idea is due to William Thurston) The Orbifold NotationĮxcerpt from Doris Schattschneider's paper A recent and more mathematically sound system is devised by J. ![]() The most widely used is the crystallographic notation adopted by the International Union of Crystallography. ![]() Various notations have been invented for the 17 wallpaper groups. Wallpaper groups: The 17 Wallpaper Groups Wallpaper Groups The 17 Wallpaper Groupsįor reference purposes, here are some tables and illustrations of the 17 wallpaper groups. ![]()
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