The matrices of the symmetrical transformations for all of the 3-dimensional Bravais lattices were found. These matrices were destined for the investigation of physical properties, of single defects in crystals, using the super-cell model. The corresponding transformations of reciprocal lattices, with a no more than 32-fold decrease in the Brillouin-zone volume, were used for the generation of special point sets for approximate numerical integration over the Brillouin zone in cubic crystals with simple, face-centered or body-centered lattices.

R.A.Evarestov, V.P.Smirnov: Journal of Physics - Condensed Matter, 1997, 9[14], 3023-31