Variances and covariances of coordinates in polar crystal systems

Relationships between positional variances and covariances that refer to different choices of origin are presented, and the situation is considered in which the uncertainties in the positioning of atoms are direction-independent and the only covariance terms are those that arise from polar aspects and nonorthogonality of the coordinate axes and from symmetry. Covariance terms can often be made small by placing the origin at a suitable centroid.