Possibility of Translational Symmetry (if Any) in Crystals

From Chaps. 3 , 4 , 5 , 6 , we have come across many evidences which clearly indicate that due to spherically symmetric nature of the Wigner–Seitz cells, the Brillouin zones (both of them are ideal representatives of mirror combination scheme) and the diffraction patterns giving rise to various sets of Braggs’ planes in the form of zone boundaries of Brillouin zones, forbid the presence of translational symmetry of any kind (either microscopic or macroscopic) in crystals, because they all possess defined origin. In fact, such spherically symmetric systems allow only the symmetries like rotation, mirror, inversion, and their compatible combinations.