Crystal Lattice and the Translation Group

A crystal lattice is a 3D array of points generated by translating the unit cell an integral number of times along each of its lattice vectors and forms the framework of the structure. Atoms or molecules may or may not be located on lattice points. The operation of displacing a unit cell parallel to itself is called a translation operation denoted by T = ia + U2b + n c. The totality of all such operations, i.e., for all integral values on JXi, n, 3, is the translation group. 

Unit cell vectors and the angles between them. 

---