The symmetry of the rotation function
D. S. Moss · Acta Crystallographica Section A Foundations of Crystallography · 1985
The correlation of two Patterson functions whose relative orientation is expressed in Eulerian coordinates gives rise to the rotation function, which possesses space-group symmetry. If the z axis is the first and last axis of Eulerian rotation then the space group of the rotation function depends only on the parity of the Patterson symmetry axes parallel and perpendicular to z. Symmetry axes in other orientations do not produce space-group effects. Nine different cross-rotation space groups occur in 16 settings. Self-rotation gives rise to additional symmetry in the rotation function and results in a further four space groups. The symmetry of a rotation function parameterized in any other coordinate system may be studied by examining the symmetries of the functions occurring in the relevant rotation matrix.