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The WignerSeitz cell (named after E. P. Wigner and Frederick Seitz) is a geometrical construction which helps in the study of crystalline material in solidstate physics. The unique property of a crystal is that its atoms are arranged in a regular, 3dimensional array, which is called a lattice. All the properties attributed to crystalline materials stem from this highly ordered structure. Such a structure exhibits discrete translational symmetry. In order to model and study such a periodic system, one needs a mathematical "handle" to describe the symmetry and hence draw conclusions about the consequences of this symmetry. The WignerSeitz cell is a means to achieve this. Definition The WignerSeitz cell around a lattice point is defined as the locus of points in space which are closer to that lattice point than to any of the other lattice points. It can be shown mathematically that a WignerSeitz Cell is a primitive cell spanning the entire Bravais lattice without leaving any gaps or holes. The WignerSeitz cell in the reciprocal lattice is known as the first Brillouin zone. Constructing the cell The cell may be chosen by first picking a lattice point. Then, lines are drawn to all nearby (closest) lattice points. At the midpoint of each line, another line is drawn normal to each of the first set of lines. In the case of a threedimensional lattice, a perpendicular plane is drawn at the midpoint of the lines between the lattice points. By using this method, the smallest area (or volume) is enclosed in this way and is called the WignerSeitz primitive cell. All area (or space) within the lattice will be filled by this type of primitive cell and will leave no gaps. General mathematical concept The general mathematical concept embodied in a WignerSeitz cell is more commonly called a Voronoi cell. Though the WignerSeitz cell in itself is not of paramount importance in direct space, it is extremely important in the reciprocal space. The WignerSeitz cell in the reciprocal space is called the Brillouin zone, which contains the information about whether a material will be a conductor, semiconductor or an insulator. Retrieved from "http://en.wikipedia.org/" 
