I agree with Ian that the fixed angles make more sense from a math point of view.
Arguments for the moving axes could involve self- and cross-rotation functions
where there are no coordinates,  or a case where the original model is
positioned with its 2-fold axis along Z, so that gamma (rotation about
the "new" Z) is rotation about the dimer axis at its position in the
new crystal, and solutions differing by 180* in gamma are equivalent.

However, amidst all this discussion of conventions, we should not forget
that Stefano's orig post included a bug report: For the same Euler angles,
pdbset and pdbcur rotate in opposite directions about the same axis.
Rotating with Stefano's angles  20 40 60, then superimposing the s
tarting model on the rotated model, gives the following:

pdbset model:
  Lsq > The 76 atoms have an r.m.s. fit of 0.001
  Lsq >  xyz(1) =     0.0637*x+   -0.7944*y+    0.6040*z+   -0.0001
  Lsq >  xyz(2) =     0.9448*x+    0.2430*y+    0.2198*z+   -0.0001
  Lsq >  xyz(3) =    -0.3214*x+    0.5567*y+    0.7660*z+    0.0001
  Lsq >  Rotation     -87.92
  Lsq >  Rossmann & Blow angles     117.58    100.96    -87.92
  Lsq >  Euler angles                30.00    -40.00   -110.00
  
  pdbcur model:
  Lsq > The 76 atoms have an r.m.s. fit of 0.000
  Lsq >  xyz(1) =     0.0637*x+    0.9448*y+   -0.3214*z+    0.0000
  Lsq >  xyz(2) =    -0.7944*x+    0.2429*y+    0.5567*z+    0.0001
  Lsq >  xyz(3) =     0.6040*x+    0.2198*y+    0.7660*z+    0.0000
  Lsq >  Rotation      87.92
  Lsq >  Rossmann & Blow angles     117.58    100.96     87.92
  Lsq >  Euler angles               -70.00    -40.00    150.00

Hmm- the Euler angles don't look right for either. Different convention?
But definitely the two programs give different results.

On 02/23/2016 06:08 AM, Ian Tickle wrote:
>
> Hi, I'm not sure what you're saying.  The two operations I described are *exactly* equivalent for *all* values of the angles.  You can show that you get the algebraically identical rotation matrix.
>
> Attached are a couple of GIF movies to demonstrate their complete equivalence (load into e.g. browser).  I made these for an online crystallography course many moons ago.
>
> Cheers
>
> -- Ian
>
>
> On 23 February 2016 at 10:38, <[log in to unmask] <mailto:[log in to unmask]>> wrote:
>
>     Sure?  With the same al-be-ga, these two operations are not equivalent, except for several special cases.  Rotations regarding to the old axes should work, but Euler's way makes the in total process more efficient?
>
>     Sent from my iPhone
>
>      > On Feb 23, 2016, at 2:02 AM, Ian Tickle <[log in to unmask] <mailto:[log in to unmask]>> wrote:
>      >
>      > So rotating the rigid body through gamma about the world z axis, then beta about the *old* (world, unrotated) y axis, then alpha about the *old* z axis gives exactly the same result as rotating the rigid body through alpha about the world z axis, then beta about the *new* (i.e. rotated with the body) y axis, then gamma about the *new* z axis, and IMO it's so much easier to visualise.
>
>