Symmetrical transformation of basic translation vectors in the supercell model of imperfect crystals and in the theory of special points of the Brillouin zone

The matrices of the symmetrical transformations for all the three-dimensional Bravais lattices are found. These matrices may be applied for the investigation of physical properties of single defects in crystals in the supercell model. The corresponding transformations of reciprocal lattices with a not more than 32-fold decrease of the Brillouin zone volume are used for the generation of special point sets for the approximative numerical integration over the Brillouin zone in cubic crystals with simple, face-centred and body-centred lattices.