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[ccp4bb]: anisotropic ellipsoids

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According to many textbooks the first three of the thermal parameters
U11 U22 U33 U12 U13 and U23 describe the displacements along the
perpendicular principal axis of the ellipsoid and the latter three give
the orientation of the principal axes with respect to the unit cell axes.
However, I can't find anywhere how U12 U13 and U23 (apparently as
direction cosini) exactly describe the orientation of the ellipsoid, say
in a cartesian system.

Any hint is appreciated (but don't suggest to try to follow the ortep

Thanks, Norbert