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-----
> From: [log in to unmask]
> [mailto:[log in to unmask]] On Behalf Of Dirk Kostrewa
> 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
> E-mail: [log in to unmask]
> *******************************************************
>
>
>
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