The definition of ‘lattice’ in one, two, and three dimensions is discussed, together with the choice of unit cell. The Bravais lattices are explained with stereoscopic illustrations, system by system, and the reciprocal lattice introduced. The law of rational intercepts and its ramifications are described, leading to an examination of preferential crystal growth planes. Transformation of unit cell vectors, zone symbols, coordinates of points in a unit cell, Miller indices and reciprocal unit cell vectors are described in detail, with examples. The Wigner–Seitz cell is discussed as an alternative crystal unit cell. Matrix representations of point groups are introduced,
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