I found some useful and interesting theorem in Ashcroft and Mermin. "For any family of lattice planes separated by a distance d,there are reciprocal lattice vectors perpendicular to the planes, the shortest of which has the length of 2pi/d. And conversely,for any reciprocal lattice vector K, there is a family of lattice planes normal to K and separated by a distance d,where 2pi/d is the length of the shortest reciprocal lattice vector parallel to K".
Family of lattice planes means a set of parallel equally spaced lattice planes, which together contains all the points of the three dimensional bravis lattice.
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