In solid state physics and mineralogy, particularly in describing crystal structure, a primitive cell is a minimum volume cell corresponding to a single lattice point. A lattice can be characterized by the geometry of its primitive cell, and a crystal can be categorized by its lattice and the atoms that lie in a primitive cell (the basis). A cell will fill all the lattice space without leaving gaps by repetition of crystal translation operations. Solid-state physics, the largest branch of condensed matter physics, is the study of rigid matter, or solids. ... Mineralogy is an earth science that involves the chemistry, crystal structure, and physical (including optical) properties of minerals. ... Rose des Sables (Sand Rose), formed of gypsum crystals In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... Volume, also called capacity, is a quantification of how much space an object occupies. ... A cherry lattice pastry A mathematical lattice is a type of partially ordered set. ...

Primitive translation vectors are used to define a crystal translation vector, , and also gives a lattice cell of smallest volume for a particular lattice. The lattice and translation vectors , , and are primitive if the atoms look the same from any lattice points using integers u₁, u₂, and u₃.

The primitive cell is defined by the primitive axes (vectors) , , and . The volume, , of the primitive cell is given by the parallelepiped from the above axes as,

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A Wigner-Seitz cell is an example of another kind of primitive cell. In certain circumstances, primitive cell is synonymous with unit cell. However, the conventional description of cubic lattices, such as body centered cubic (BCC) and face centered cubic (FCC) lattices, relies on a cubic unit cell. In the BCC and FCC cases, the primitive cell is distinct from this conventional unit cell. A Wigner-Seitz cell, in solid state physics, is a primitive lattice cell. ... Rose des Sables (Sand Rose), formed of gypsum crystals In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... In crystallography, the cubic crystal system (or isometric crystal system) is the most symmetric of the 7 crystal systems. ...

The general mathematical concept behind the primitive cell is termed the fundamental domain or the Voronoi cell. The primitive cell of the reciprocal lattice in momentum space is called the Brillouin zone. In mathematics, given a lattice Γ in a Lie group G, a fundamental domain is a set D of representatives for the cosets G/Γ, that is also a well-behaved set topologically, in a sense that can be made precise in one of several ways. ... This is the Voronoi diagram of a random set of points in the plane (all points lie within the image). ... In crystallography, the reciprocal lattice of a Bravais lattice is the set of all vectors K such that for all lattice point position vectors R. The reciprocal lattice is itself a Bravais lattice, and the reciprocal of the reciprocal lattice is the original lattice. ... Frequency domain is a term used to describe the analysis of mathematical functions with respect to frequency. ... In mathematics and solid state physics, the first Brillouin zone is the primitive cell in the reciprocal lattice in momentum space. ...