Dear CCP4ers,
I've asked you about symmetry in stereographic projections of self-
rotation functions, because I have in a monoclinic space group with
beta=97 a peak for a NCS 7-fold axis at Phi=83, Psi=90, Kappa=51.4.
In this self-rotation function, calculated with GLRF, the monoclinic
b-axis is oriented from south-pole to north-pole. Thus, with Psi=90,
the 7-fold lies in the a,c-plane, and I was wondering wether it
points along the c-axis by some symmetry element, since 83=180-97.
Pierre Rizkallah pointed to the fact that the self-rotation function
is calculated in Patterson space which has an inversion centre, and
Ian Tickle has pointed me to the POLARRFN documentation that
discusses some of these symmetries. From this, I can, in my case,
construct the following symmetry-equivalent positions:
(1) Original Peak: Phi, Psi, Kappa ---
> 83, 90, 51.4
(2) General equivalent position: 180+Phi, 180-Psi, -Kappa --->
263, 90, -51.4
(3) Crystallographic Dyad || Poles: 180+Phi, Psi, Kappa --->
263, 90, 51.4
(4) (3) combined with (2): Phi, 180-Psi, -Kappa ---
> 83, 90, -51.4
Thus, none of these combinations gives a Phi-angle of 97 degrees.
However, meanwhile Liang Tong, the author of GLRF, explained to me,
that in his convention, a positive Phi angle goes from +X (=a) to -Z
(=-c*), which means that Phi=83 points really along the (-)c-axis
(thus confirming my initial hypothesis).
7-fold
/
/
/
b-------------- a
/|
/ |
/ |
/ |
c c*
So, many thanks to all of you who replied and helped me to solve this
puzzle!
I would still be interested in a textbook or paper discussing
symmetry in stereographic projections, though ...
Best regards,
Dirk.
Am 22.11.2007 um 14:40 schrieb Dirk Kostrewa:
> 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]
> *******************************************************
>
>
*******************************************************
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]
*******************************************************
