A primitive cell is a unit cell built on the basis vectors of a 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.
It contains only one lattice point and its volume is equal to the triple scalar product (a, b, c).
Non-primitive bases are used conventionally to describe centered lattices. In that case, the unit cell is a multiple cell and it contains more than one lattice point. The multiplicity of the cell is given by the ratio of its volume to the volume of a primitive cell.
- Section 8.1 of International Tables of Crystallography, Volume A