# Primitive cell

A **primitive cell** is a unit cell built on the primitive basis of the direct lattice, namely a crystallographic basis of the vector lattice L such that every lattice vector t of L may be obtained as an integral linear combination of the basis vectors, a, b, c.

Used predominantly in geometry, solid state physics, and mineralogy, particularly in describing crystal structure, a primitive cell is a minimum volume cell corresponding to a single lattice point of a structure with translational symmetry in 2 dimensions, 3 dimensions, or other dimensions. A lattice can be characterized by the geometry of its *primitive cell*.

The primitive cell is a fundamental domain with respect to translational symmetry only. In the case of additional symmetries a fundamental domain is smaller.

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.

*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 , , and .

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