Hi Dirk
There's a useable (though slightly incomplete) description of the
symmetry of SRF's in the POLARRFN doc, though this only talks about the
symmetry of the stereographic projection itself and then only about the
effect of crystallographic dyads. Higher order rotations about z will
obviously produce the same symmetry in the SRF. However higher order
rotations about other axes (e.g. 3-folds in cubic) will not generate
symmetry in the SRF, the peaks will be there of course but in general
positions in spherical polar co-ords.
In the case you describe, if there were the symmetry phi'=180-phi
wouldn't you expect to see both peaks?
The only crystallographic symmetry in monoclinic with z||b is
phi'=180+phi, so in your case it would appear that your 7-fold NCS axis
is parallel to c* not c.
-- Ian
-----Original Message-----
Sent: 22 November 2007 13:41
To: CCP4BB
Subject: Symmetry of crystallographic stereographic projections?
Dear CCP4ers,
does any of you have a good reference describing the symmetry
of crystallographic stereographic projections? There is a lot
of literature describing rotational symmetry in Eulerian
angular space, but I'm not aware of any for polar angles. In
particular, I've calculated a self-rotation function for a
crystal in space group C2 with a monoclinic beta-angle of 97
degrees in a convention where Phi is the angle from the
x-axis (=a-axis) and Psi is the angle from the monoclinic
b-axis. I get a beautiful peak for a seven-fold rotation axis
at Phi=83 degrees and Psi=90 degrees. I think that the
seven-fold NCS-axis should point along the crystallographic
c-axis, but then I would expect Phi=97 and Psi=90.
Presumably, there must be a symmetry with the term Phi' =
180-Phi, but I would like to _know_ it. I would be grateful
for any pointer to a good reference describing symmetry in
crystallographic stereographic projections, also for future cases.
Best regards,
Dirk.
*******************************************************
Dirk Kostrewa
Gene Center, A 5.07
Ludwig-Maximilians-University
Feodor-Lynen-Str. 25
81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
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