ABSTRACT
Solids are built up from arrangements of atoms. In crystals these arrangements must show regularity and there must be long-range order such that the pattern of the atoms repeats regularly throughout the crystal. If the atoms are all of the same type, and of the same size, they will fit together in a close-packing configuration. The hexagonal cell contains two atoms because the eight corner atoms are again shared between eight cells and there is one atom inside the cell. The five lattices constitute four crystal systems as the two rectangular lattices are included in one crystal system. A four-index system for crystallographic directions can be used for hexagonal crystals. The cubic system consisting of a cell of sides of equal length, orthogonal to each other, is the three-dimensional equivalent of the square. Rotational symmetry can be twofold, threefold, fourfold or sixfold.
