and so on for the other primitive vectors. The crystallographer's definition has the advantage that the definition of b 1 is just the reciprocal magnitude of a 1 in the direction of a 2 × × a 3 , dropping the factor of 2 π π . This can simplify certain mathematical manipulations, and expresses reciprocal lattice dimensions in units of spatial frequency. It is a matter of taste which definition of the lattice is used, as long as the two are not mixed.