Crystal Structure and Dynamics
2012
3 Wallpaper groups 8 3.1 A few new concepts for Wallpaper Groups . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Lattices and the “translation set” . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Bravais lattices in 2D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3.1 Oblique system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3.2 Rectangular system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3.3 Square system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3.4 Hexagonal system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Primitive, asymmetric and conventional Unit cells in 2D . . . . . . . . . . . . . . . 11 3.5 The 17 wallpaper groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.6 Analyzing wallpaper and other 2D art using wallpaper groups . . . . . . . . . . . . 12
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