Unit cell
base of crystal structure
In geometry and crystallography, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessarily have unit size, or even a particular size at all. Rather, the primitive cell is the closest analogy to a unit vector, since it has a determined size for a given lattice and is the basic building block from which larger cells are constructed. Geometrically, this is a special case of a fundamental domain of a group (the translation symmetries) acting on a topological space (Euclidean space).
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 unit cell, which is a section of the tiling (a parallelogram or parallelepiped) that generates the whole tiling using only translations.
There are two special cases of the unit cell: the primitive cell and the conventional cell. The primitive cell is a unit cell corresponding to a single lattice point; it is the smallest possible unit cell. In some cases, the full symmetry of a crystal structure is not obvious from the primitive cell, in which case a conventional cell may be used. A conventional cell (which may or may not be primitive) is the smallest unit cell with the full symmetry of the lattice and may include more than one lattice point.
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