There is a useful article in Computational Crystallography Newsletter 2011, 2, 
12-14 that gives some background into the issues surrounding the H3 and H32 
symbols:

 "Fuzzy space group symbols: H3 and H32

http://www.phenix-online.org/newsletter/CCN_2011_01.pdf

Cheers,

Richard

Dr Richard Gildea
Data Analysis Scientist
Tel: +441235 77 8078

Diamond Light Source Ltd.
Diamond House
Harwell Science & Innovation Campus
Didcot
Oxfordshire
OX11 0DE
________________________________
From: CCP4 bulletin board <CCP4BB@JISCMAIL.AC.UK> on behalf of David Vizarraga 
Revuelto <dvr...@ibmb.csic.es>
Sent: 22 July 2020 12:20
To: CCP4BB@JISCMAIL.AC.UK <CCP4BB@JISCMAIL.AC.UK>
Subject: [ccp4bb] Question about P3, H3 and R3 space groups

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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