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We present sets of special points in the Brillouin zone from which the average over the Brillouin zone of a periodic function of wave vector (e.g., energy, charge density, dipole matrix elements, etc.) can be determined in a simple and accurate way once the values of the function at these points are specified. We discuss a method for generating the special-point sets and apply it to the case of crystals with cubic and hexagonal Bravais lattices.
Chadi et al. (Sat,) studied this question.