On the separation of the unknown parameters of the problem of crystal-structure analysis

The problem of crystal-structure analysis can be given a form which exhibits dual quasi-symmetry. The orthogonality of the Fourier waves and the non-interpenetration of the atoms play a complementary role; this holds not only formally but also with respect to the separation of the coordinates of the atoms and the phases of the structure factors. The remarkable fact that the Patterson function is described by a convolution in direct space, while Sayre's equation is a convolution in reciprocal space may be understood as a part of the symmetry.