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In solid state physics, a primitive cell is a minimum volume cell (a unit cell) corresponding to a single lattice point of a structure with discrete translational symmetry. The concept is used particularly in describing crystal structure in two and three dimensions, though it makes sense in all dimensions. A lattice can be characterized by the geometry of its primitive cell.
The primitive cell is a primitive unit. A primitive unit is a section of the tiling (usually a parallelogram or a set of neighboring tiles) that generates the whole tiling using only translations, and is as small as possible.
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 2-dimensional primitive cell is a parallelogram, which in special cases may have orthogonal angles, or equal lengths, or both.
2-dimensional primitive cells
Parallelogram Rhombus
(Orthorhombic) (Monocinic)
Rectangle Square
(Orthorhombic) (Tetragonal)
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.
A 3-dimensional primitive cell is a parallelepiped, which in special cases may have orthogonal angles, or equal lengths, or both.
3-dimensional primitive cells
Parallelepiped Oblique rhombic prism Oblique rectangular prism
(Triclinic) (Monoclinic) (Monoclinic)
Right rhombic prism (Orthorhombic)
Rectangular cuboid (Orthorhombic) Square cuboid (Tetragonal)
Trigonal trapezohedron (Rhombohedral)
Cube (Cubic)