Wigner–Seitz cell

A primitive cell made of all points closer to one lattice point than to any other. Its boundaries are perpendicular bisectors between that lattice point and neighboring lattice points.

Voronoi diagram: A partition of space into regions nearest to specified seed points. The Wigner–Seitz construction is the Voronoi partition generated by lattice points.
Bravais lattice: An infinite array of points generated by translations along a finite set of lattice vectors. Wigner–Seitz cells are constructed from the points of a Bravais lattice.
Coordination number: The number of nearest neighbors surrounding a specified atom or lattice site. The cell’s faces correspond to neighboring lattice sites, making their coordination geometrically apparent.
Parallelepiped cell: A cell bounded by pairs of parallel planes and spanned by lattice vectors. Unlike this vector-defined cell, the Wigner–Seitz shape follows nearest-point boundaries.
Perpendicular bisector: The line or plane of points equidistant from two specified points. Each cell face lies on a bisector between the central lattice point and a neighbor.
Primitive cell: A region that tiles a lattice by translation and contains exactly one lattice point per cell on average. The Wigner–Seitz cell is a primitive cell selected by a nearest-point rule.
Miller indices: A notation for the orientation of planes in a crystal lattice. Cell-face orientations can be described using the same crystallographic plane notation.
Conventional cell: A unit cell chosen to display a crystal lattice’s symmetry, sometimes containing multiple lattice points. Conventional cells emphasize symmetry, while the Wigner–Seitz cell is always primitive.
Brillouin zone: A Wigner–Seitz cell of a reciprocal lattice, used to represent crystal wavevectors. Applying the same nearest-point construction in reciprocal space gives the first Brillouin zone.
Lattice vector: A vector connecting one point of a lattice to another. Vectors to neighboring lattice points determine the bisectors that bound the cell.

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Eugene WignerBroader topic: This construction uses symmetry to define a fundamental region in crystal lattices.