The alignment of point-group symmetry operations with a cluster of points in three-dimensional space is made by a minimization of the sum distortion attributable to the various symmetry operationsa least sum of pairs of the vectors V and V*[A], representing the original and transformed, assigned structures. As any residual rotational and transformational displacement will contribute to dissymmetric distortion, this correct alignment of the atomic structure is important to attain consistent values. The existence of separated 'basins' in even simple analyses requires either a basin-hopping algorithm or choice of multiple perpendicular starting pointsthe use of six perpendicular orientations was found to be sufficient to achieve the global minima in most cases.