How about this (may be way off base): Any transformation can be seen either as moving of the coordinates in a fixed coordinate system, or as a "change of coordinates" and expressing the position of the same object with respect to the new coordinates.
In molecular replacement it is convenient to think of it as a change in coordinates, with the old coordinates being along the old cell axes (or some orthogonalization of them) and the new coordinates along the new cell. gamma is rotation about z in the old cell, beta is the nose-down you do before plopping it into the new cell, and alpha is rotation about the z axis in the new cell. Take a physical example: My MR model is a proper dimer with its dimer 2-fold along Z. Lets drive it over into the new cell according to rotation function results. I see there are two equal results with gamma differing by 180. That's because my model has two-fold symmetry about z (old z, that is). I pick either gamma, rotate about my models axis that much, then rotate about x by beta (but mind you, x doesn't pass through my model the way it used to- this is "new x". Now I assume I am in the new coordinate system and rotate about z again- only this time z is not along my dimer axis. The new cell has 3-fold crystallograhic symmetry about z, so I see the rotsol alpha is 3-fold degenerate. Rotation about z is mathematically rotation about z, whether it be the "old" z or "new" z, i.e. the matrix has a special simple form like cos sin 0 -sin cos 0 0 0 1 Otherwise there would be no point in factoring single matrix into three equally general matrices. Ed
