Fast Fourier transforms for space groups containing rotation axes of order three and higher

Methods are described for exploiting the symmetry of uniaxial space groups containing rotation axes of order three and higher to improve the efficiency of computation of Fourier transforms. Mapping a symmetrical two-dimensional section into four dimensions enables the selection of non-contiguous asymmetric units over which fast Fourier transforms can be performed that reduce the computation time by a factor of approximately the order of the rotation axis. The application of the procedure to plane group p3 and its extension to p4 and p6 are described.