Hi David

The problem is that the PDB incorrectly used the H lattice symbol (without
consulting any crystallographers AFAIK) for the hexagonal R-centred cell
when it had already been in use for many years for the triply-primitive
setting of P3, so now we have this confusion between MX & XRD/powder
usage.  It's probably now too late to do anything about it.  Simply put: in
XRD/powder software H3 is #143 as originally specified in IUCr Int. Tab.;
in MX software H3 is #146.

What should have been used are the Hermann-Mauguin symbols for the two R3
cells: R3:r and R3:h (see the syminfo.lib file).

This is a constant confusion between the standard symbol (i.e. one of the
230 space-groups in their standard settings) and the setting symbols.
Other common examples are space group #5 with standard symbol C2 which has
a number of alternative settings A121, B112, C121, I121 etc., and standard
symbol P21212 with settings P22121, P21221 and P21212, all of which are
equally valid.  The conventional IUCr choice of setting is determined by
the relative cell lengths (as far as possible c >= b >= a) and the cell
angle (which in monoclinic cells should always be chosen >= 90 and closest
to 90).  In practical crystallography it's the setting symbol that matters;
the standard symbol is relevant only for classification, so in practice
only the setting symbols should be used/

Cheers

--  Ian


On Wed, 22 Jul 2020 at 12:32, David Vizarraga Revuelto <dvr...@ibmb.csic.es>
wrote:

> Dear all,
>
> Let me ask a question about the P3,H3, R3 space group annotations.
> I had the idea that H3 was the recommended annotation for the hexagonal
> representation of R3 (space group number 146). However, in the Birbeck
> space groups web page (attached) H3 is associated with the space group
> number 143 corresponding to P3. Similarly for all the other H groups
> assigned in the page. Moreover in the web page none of the R space groups
> is assigned to an H annotation.
>
> H3 corresponds to 143 or  to 146?
> Is there a space group 154 annotated as H32 1 2?
>
> Many thanks.
>
>
>
> "Note that the figure showing the relationship between primitive and
> R-centred rhomohedral cells with hexagonal axes is clickable
>
> Rhombohedral with Hexagonal axes
> 146. *R* 3 <http://img.chem.ucl.ac.uk/sgp/large/146bz1.htm> 148. *R* -3
> <http://img.chem.ucl.ac.uk/sgp/large/148bz1.htm> 155. *R* 3 2
> <http://img.chem.ucl.ac.uk/sgp/large/155bz1.htm> 160. *R* 3 *m*
> <http://img.chem.ucl.ac.uk/sgp/large/160bz1.htm> 161. *R* 3 *c*
> <http://img.chem.ucl.ac.uk/sgp/large/161bz1.htm> 166. *R* -3 *m*
> <http://img.chem.ucl.ac.uk/sgp/large/166bz1.htm>
> 167. *R* -3 *c* <http://img.chem.ucl.ac.uk/sgp/large/167bz1.htm>
> H-centred Trigonal
> 143. *H* 3 <http://img.chem.ucl.ac.uk/sgp/large/143bz1.htm> 144. *H* 31
> <http://img.chem.ucl.ac.uk/sgp/large/144bz1.htm> 145. *H* 32
> <http://img.chem.ucl.ac.uk/sgp/large/145bz1.htm> 147. *H* -3
> <http://img.chem.ucl.ac.uk/sgp/large/147bz1.htm> 149. *H* 3 2 1
> <http://img.chem.ucl.ac.uk/sgp/large/149bz1.htm> 150. *H* 3 1 2
> <http://img.chem.ucl.ac.uk/sgp/large/150bz1.htm>
> 151. *H* 31 2 1 <http://img.chem.ucl.ac.uk/sgp/large/151bz1.htm> 152. *H*
>  31 1 2 <http://img.chem.ucl.ac.uk/sgp/large/152bz1.htm> 153. *H* 32 2 1
> <http://img.chem.ucl.ac.uk/sgp/large/153bz1.htm> 154. *H* 32 1 2
> <http://img.chem.ucl.ac.uk/sgp/large/154bz1.htm> 156. *H* 3 1 *m*
> <http://img.chem.ucl.ac.uk/sgp/large/156bz1.htm> 157. *H* 3 *m* 1
> <http://img.chem.ucl.ac.uk/sgp/large/157bz1.htm>
> 158. *H* 3 1 *c* <http://img.chem.ucl.ac.uk/sgp/large/158bz1.htm> 159. *H*
>  3 *c* 1 <http://img.chem.ucl.ac.uk/sgp/large/159bz1.htm> 162. *H* -3 *m*
>  1 <http://img.chem.ucl.ac.uk/sgp/large/162bz1.htm> 163. *H* -3 *c* 1
> <http://img.chem.ucl.ac.uk/sgp/large/163cz1.htm> 164. *H* -3 1 *m*
> <http://img.chem.ucl.ac.uk/sgp/large/164bz1.htm> 165. *H* -3 1 *c*
> <http://img.chem.ucl.ac.uk/sgp/large/165cz1.htm>
>
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