Re: [ccp4bb] Question about P3, H3 and R3 space groups

[Eleanor Dodson]

d Laboratories
>>> 20 Gordon Street
>>> London WC1H 0AJ
>>> +44 (0) 20 7679 1004 (laboratory)
>>> +44 (0) 7981 875 829 (cell/mobile)
>>> j.k.cockcr...@ucl.ac.uk or jeremyk...@gmail.com
>>> http://img.chem.ucl.ac.uk/www/cockcroft/homepage.htm
>>> ***
>>> 6 Wellington Road
>>> Horsham
>>> West Sussex
>>> RH12 1DD
>>> +44 (0) 1403 256946 (home)
>>> ***
>>>
>>>
>>> On Wed, 22 Jul 2020 at 14:51, Nicholas Keep 
>>> wrote:
>>>
>>>>
>>>>
>>>>
>>>>  Forwarded Message 
>>>> Subject: Re: [ccp4bb] Question about P3, H3 and R3 space groups
>>>> Date: Wed, 22 Jul 2020 14:41:27 +0100
>>>> From: Eleanor Dodson <176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk>
>>>> <176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk>
>>>> Reply-To: Eleanor Dodson 
>>>> 
>>>> To: CCP4BB@JISCMAIL.AC.UK
>>>>
>>>> But surely P3 symmetry ' cell ( a,a,c 90 90 120) with origin shifts
>>>> (⅓,⅔,0), +(⅔,⅓,0) can just be indexed as P3 with
>>>> cell (a/sqrt(3), a/sqrt(3), c, 90 90 120) ??
>>>> Eleanor
>>>>
>>>> On Wed, 22 Jul 2020 at 14:32, Nicholas Keep <
>>>> n.k...@mail.cryst.bbk.ac.uk> wrote:
>>>>
>>>>> I have an answer from Jeremy Cockcroft the author of the 'Birkbeck'
>>>>> Tables. Actually Jeremy has been at UCL for a decade or so and they are
>>>>> hosted from their
>>>>>
>>>>> Nick
>>>>>
>>>>> In answer to the question regarding the use of R and H for trigonal
>>>>> space groups, the letters refer to two distinct types of lattice centring
>>>>> symmetry operation, namely +(⅓,⅔,⅔), +(⅔,⅓,⅓) and +(⅓,⅔,0), +(⅔,⅓,0),
>>>>> respectively. For the subset of rhombohedral space groups, the symbol R
>>>>> should always be used.  When the alternative unit cell with a=b=c and
>>>>> α=β=γ is chosen, this cell corresponds to a primitive Bravais lattice, but
>>>>> the label P is not used as this would result in confusion with
>>>>> non-rhombohedral space groups.  (The choice of symmetry operators for
>>>>> rhombohedral space groups is wholly dependent of the choice of unit cell,
>>>>> i.e. hexagonal versus rhombohedral, so there is no ambiguity if the unit
>>>>> cell is specified.)
>>>>>
>>>>> For the non-rhombohedral space groups, it may occasionally be
>>>>> convenient to choose a larger H-centred unit cell that is not the usual
>>>>> primitive P one.  (The use of larger unit cells is quite common for
>>>>> systems that undergo phase transformations as it may enable the
>>>>> crystallographer to keep the contents of the unit cell the same in both
>>>>> phases.)  Note that the use of an H-centred lattice switches the
>>>>> order of the symmetry elements in these space group symbols, e.g. P312
>>>>> becomes H321.
>>>>>
>>>>> I am not aware of any changes to this convention, which I believe has
>>>>> a long history.  However, it is possible that the letter H has been
>>>>> used unwittingly for other purposes.
>>>>>
>>>>> Jeremy Karl Cockcroft
>>>>>
>>>>>
>>>>> --
>>>>>
>>>>> NOTE NEW PHONE NUMBER JULY 2020
>>>>>
>>>>> Prof Nicholas H. Keep
>>>>> Executive Dean of School of Science
>>>>> Professor of Biomolecular Science
>>>>> Crystallography, Institute for Structural and Molecular Biology,
>>>>> Department of Biological Sciences
>>>>> Birkbeck,  University of London,
>>>>> Malet Street,
>>>>> Bloomsbury
>>>>> LONDON
>>>>> WC1E 7HX
>>>>>
>>>>> Office G54a
>>>>>
>>>>> Dean Email;   scid...@bbk.ac.uk
>>>>> Dept email n.k...@mail.cryst.bbk.ac.uk
>>>>> Telephone 020-3926-3475  (Will contact me at home if working as well as 
>>>>> my office)
>>>>>
>>>>> If you want to access me in person you have to come to the 
>>>>> crystallography entrance
>>>>> and ring me or the department office from the internal phone by the door
>>>>>
>>>>>
>>>>> --
>>>>>
>>>>> To unsubscribe from the CCP4BB list, click the following link:
>>>>> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1
>>>>>
>>>>
>>>> --
>>>>
>>>> To unsubscribe from the CCP4BB list, click the following link:
>>>> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1
>>>>
>>>
>> --
>>
>> To unsubscribe from the CCP4BB list, click the following link:
>> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1
>>
>
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Re: [ccp4bb] Question about P3, H3 and R3 space groups

[James Holton]

*


On Wed, 22 Jul 2020 at 14:51, Nicholas Keep
mailto:n.k...@mail.cryst.bbk.ac.uk>> wrote:




     Forwarded Message 
Subject:Re: [ccp4bb] Question about P3, H3 and R3 space
groups
Date:   Wed, 22 Jul 2020 14:41:27 +0100
From:   Eleanor Dodson
<176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk>
<mailto:176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk>
Reply-To:   Eleanor Dodson 
<mailto:eleanor.dod...@york.ac.uk>
To: CCP4BB@JISCMAIL.AC.UK <mailto:CCP4BB@JISCMAIL.AC.UK>



But surely P3 symmetry ' cell ( a,a,c 90 90 120) with
origin shifts (⅓,⅔,0), +(⅔,⅓,0) can just be indexed as P3
with
cell (a/sqrt(3), a/sqrt(3), c, 90 90 120) ??
Eleanor

On Wed, 22 Jul 2020 at 14:32, Nicholas Keep
mailto:n.k...@mail.cryst.bbk.ac.uk>> wrote:

I have an answer from Jeremy Cockcroft the author of
the 'Birkbeck' Tables. Actually Jeremy has been at UCL
for a decade or so and they are hosted from their

Nick

In answer to the question regarding the use of R and H
for trigonal space groups, the letters refer to two
distinct types of lattice centring symmetry operation,
namely +(⅓,⅔,⅔), +(⅔,⅓,⅓) and +(⅓,⅔,0), +(⅔,⅓,0),
respectively. For the subset of rhombohedral space
groups, the symbol R should always be used.When the
alternative unit cell with a=b=c and α=β=γ is chosen,
this cell corresponds to a primitive Bravais lattice,
but the label P is not used as this would result in
confusion with non-rhombohedral space groups. (The
choice of symmetry operators for rhombohedral space
groups is wholly dependent of the choice of unit cell,
i.e. hexagonal versus rhombohedral, so there is no
ambiguity if the unit cell is specified.)

For the non-rhombohedral space groups, it may
occasionally be convenient to choose a larger
H-centred unit cell that is not the usual primitive P
one.(The use of larger unit cells is quite common for
systems that undergo phase transformations as it may
enable the crystallographer to keep the contents of
the unit cell the same in both phases.)Note that the
use of an H-centred lattice switches the order of the
symmetry elements in these space group symbols, e.g.
P312 becomes H321.

I am not aware of any changes to this convention,
which I believe has a long history. However, it is
possible that the letter H has been used unwittingly
for other purposes.

Jeremy Karl Cockcroft


-- 


NOTE NEW PHONE NUMBER JULY 2020

Prof Nicholas H. Keep
Executive Dean of School of Science
Professor of Biomolecular Science
Crystallography, Institute for Structural and Molecular Biology,
Department of Biological Sciences
Birkbeck,  University of London,
Malet Street,
Bloomsbury
LONDON
WC1E 7HX

Office G54a

Dean Email; scid...@bbk.ac.uk  <mailto:scid...@bbk.ac.uk>
Dept emailn.k...@mail.cryst.bbk.ac.uk  
<mailto:n.k...@mail.cryst.bbk.ac.uk>
Telephone 020-3926-3475  (Will contact me at home if working as 
well as my office)

If you want to access me in person you have to come to the 
crystallography entrance
and ring me or the department office from the internal phone by 
the door





To unsubscribe from the CCP4BB list, click the
following link:
https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1






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To unsubscribe from the CCP4BB list, cli

Re: [ccp4bb] Question about P3, H3 and R3 space groups

[Ian Tickle]

The original reference for the H cell is the very first edition of Int.
Tab.:

Hermann, C. (1935).  Internationale Tabellen zur Bestimmung von
Kristallstrukturen.  Berlin: Gebrueder Borntraeger.

Cheers

-- Ian


On Wed, 22 Jul 2020 at 17:34, Eleanor Dodson <
176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk> wrote:

> Well - yes . I am a true devotee of doctored cells to match something
> already in existence in a higher symmetry which has become approximate in
> some new manifestation! But I hadnt realised there were official versions
> of doctoring..
> Eleanor
>
> On Wed, 22 Jul 2020 at 16:29, Jeremy Karl Cockcroft 
> wrote:
>
>> Dear Eleanor,
>> What you say is absolutely spot-on! An H3 cell can be reduced down to the
>> smaller P3 cell as you pointed out.
>>
>> However, sometimes it may be useful to use a larger unit cell. I can't
>> give an example for trigonal space groups or from protein crystallography,
>> but in a recent paper, I used a unit cell in C-1 (i.e. a doubled P-1
>> triclinic cell) as this related to the C-centred monoclinic cell as
>> exhibited in a higher temperature phase. I could have used P-1, but I knew
>> that chemists would see the relationship between the phases more easily by
>> using an enlarged cell. I have done this sort of thing many times, e.g. I
>> used F2/d for the low temperature phase of DI (HI) many years ago instead
>> of C2/c as this related to the face-centred cubic form. As I am interested
>> in phase transitions, I  tabulated a range of space-group settings for
>> enlarged unit cells on my site.
>>
>> I am not sure that this will make the CCP4 list as I am not subscribed to
>> it - please feel free to echo it on there.
>> Best regards,
>> Jeremy Karl.
>> ***
>> Dr Jeremy Karl Cockcroft
>> Department of Chemistry
>> (University College London)
>> Christopher Ingold Laboratories
>> 20 Gordon Street
>> London WC1H 0AJ
>> +44 (0) 20 7679 1004 (laboratory)
>> +44 (0) 7981 875 829 (cell/mobile)
>> j.k.cockcr...@ucl.ac.uk or jeremyk...@gmail.com
>> http://img.chem.ucl.ac.uk/www/cockcroft/homepage.htm
>> ***
>> 6 Wellington Road
>> Horsham
>> West Sussex
>> RH12 1DD
>> +44 (0) 1403 256946 (home)
>> ***
>>
>>
>> On Wed, 22 Jul 2020 at 14:51, Nicholas Keep 
>> wrote:
>>
>>>
>>>
>>>
>>>  Forwarded Message 
>>> Subject: Re: [ccp4bb] Question about P3, H3 and R3 space groups
>>> Date: Wed, 22 Jul 2020 14:41:27 +0100
>>> From: Eleanor Dodson <176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk>
>>> <176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk>
>>> Reply-To: Eleanor Dodson 
>>> 
>>> To: CCP4BB@JISCMAIL.AC.UK
>>>
>>> But surely P3 symmetry ' cell ( a,a,c 90 90 120) with origin shifts
>>> (⅓,⅔,0), +(⅔,⅓,0) can just be indexed as P3 with
>>> cell (a/sqrt(3), a/sqrt(3), c, 90 90 120) ??
>>> Eleanor
>>>
>>> On Wed, 22 Jul 2020 at 14:32, Nicholas Keep 
>>> wrote:
>>>
>>>> I have an answer from Jeremy Cockcroft the author of the 'Birkbeck'
>>>> Tables. Actually Jeremy has been at UCL for a decade or so and they are
>>>> hosted from their
>>>>
>>>> Nick
>>>>
>>>> In answer to the question regarding the use of R and H for trigonal
>>>> space groups, the letters refer to two distinct types of lattice centring
>>>> symmetry operation, namely +(⅓,⅔,⅔), +(⅔,⅓,⅓) and +(⅓,⅔,0), +(⅔,⅓,0),
>>>> respectively. For the subset of rhombohedral space groups, the symbol R
>>>> should always be used.  When the alternative unit cell with a=b=c and
>>>> α=β=γ is chosen, this cell corresponds to a primitive Bravais lattice, but
>>>> the label P is not used as this would result in confusion with
>>>> non-rhombohedral space groups.  (The choice of symmetry operators for
>>>> rhombohedral space groups is wholly dependent of the choice of unit cell,
>>>> i.e. hexagonal versus rhombohedral, so there is no ambiguity if the unit
>>>> cell is specified.)
>>>>
>>>> For the non-rhombohedral space groups, it may occasionally be
>>>> convenient to choose a larger H-centred unit cell that is not the usual
>>>> primitive P one.  (The use of larger unit cells is quite common for
>&

Re: [ccp4bb] Question about P3, H3 and R3 space groups

[Eleanor Dodson]

Well - yes . I am a true devotee of doctored cells to match something
already in existence in a higher symmetry which has become approximate in
some new manifestation! But I hadnt realised there were official versions
of doctoring..
Eleanor

On Wed, 22 Jul 2020 at 16:29, Jeremy Karl Cockcroft 
wrote:

> Dear Eleanor,
> What you say is absolutely spot-on! An H3 cell can be reduced down to the
> smaller P3 cell as you pointed out.
>
> However, sometimes it may be useful to use a larger unit cell. I can't
> give an example for trigonal space groups or from protein crystallography,
> but in a recent paper, I used a unit cell in C-1 (i.e. a doubled P-1
> triclinic cell) as this related to the C-centred monoclinic cell as
> exhibited in a higher temperature phase. I could have used P-1, but I knew
> that chemists would see the relationship between the phases more easily by
> using an enlarged cell. I have done this sort of thing many times, e.g. I
> used F2/d for the low temperature phase of DI (HI) many years ago instead
> of C2/c as this related to the face-centred cubic form. As I am interested
> in phase transitions, I  tabulated a range of space-group settings for
> enlarged unit cells on my site.
>
> I am not sure that this will make the CCP4 list as I am not subscribed to
> it - please feel free to echo it on there.
> Best regards,
> Jeremy Karl.
> ***
> Dr Jeremy Karl Cockcroft
> Department of Chemistry
> (University College London)
> Christopher Ingold Laboratories
> 20 Gordon Street
> London WC1H 0AJ
> +44 (0) 20 7679 1004 (laboratory)
> +44 (0) 7981 875 829 (cell/mobile)
> j.k.cockcr...@ucl.ac.uk or jeremyk...@gmail.com
> http://img.chem.ucl.ac.uk/www/cockcroft/homepage.htm
> ***
> 6 Wellington Road
> Horsham
> West Sussex
> RH12 1DD
> +44 (0) 1403 256946 (home)
> ***
>
>
> On Wed, 22 Jul 2020 at 14:51, Nicholas Keep 
> wrote:
>
>>
>>
>>
>>  Forwarded Message 
>> Subject: Re: [ccp4bb] Question about P3, H3 and R3 space groups
>> Date: Wed, 22 Jul 2020 14:41:27 +0100
>> From: Eleanor Dodson <176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk>
>> <176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk>
>> Reply-To: Eleanor Dodson 
>> 
>> To: CCP4BB@JISCMAIL.AC.UK
>>
>> But surely P3 symmetry ' cell ( a,a,c 90 90 120) with origin shifts
>> (⅓,⅔,0), +(⅔,⅓,0) can just be indexed as P3 with
>> cell (a/sqrt(3), a/sqrt(3), c, 90 90 120) ??
>> Eleanor
>>
>> On Wed, 22 Jul 2020 at 14:32, Nicholas Keep 
>> wrote:
>>
>>> I have an answer from Jeremy Cockcroft the author of the 'Birkbeck'
>>> Tables. Actually Jeremy has been at UCL for a decade or so and they are
>>> hosted from their
>>>
>>> Nick
>>>
>>> In answer to the question regarding the use of R and H for trigonal
>>> space groups, the letters refer to two distinct types of lattice centring
>>> symmetry operation, namely +(⅓,⅔,⅔), +(⅔,⅓,⅓) and +(⅓,⅔,0), +(⅔,⅓,0),
>>> respectively. For the subset of rhombohedral space groups, the symbol R
>>> should always be used.  When the alternative unit cell with a=b=c and
>>> α=β=γ is chosen, this cell corresponds to a primitive Bravais lattice, but
>>> the label P is not used as this would result in confusion with
>>> non-rhombohedral space groups.  (The choice of symmetry operators for
>>> rhombohedral space groups is wholly dependent of the choice of unit cell,
>>> i.e. hexagonal versus rhombohedral, so there is no ambiguity if the unit
>>> cell is specified.)
>>>
>>> For the non-rhombohedral space groups, it may occasionally be convenient
>>> to choose a larger H-centred unit cell that is not the usual primitive P
>>> one.  (The use of larger unit cells is quite common for systems that
>>> undergo phase transformations as it may enable the crystallographer to keep
>>> the contents of the unit cell the same in both phases.)  Note that the
>>> use of an H-centred lattice switches the order of the symmetry elements in
>>> these space group symbols, e.g. P312 becomes H321.
>>>
>>> I am not aware of any changes to this convention, which I believe has a
>>> long history.  However, it is possible that the letter H has been used
>>> unwittingly for other purposes.
>>>
>>> Jeremy Karl Cockcroft
>>>
>>>
>>> --
>>>
>>> NOTE NEW PHONE NUMBER JULY 20

Re: [ccp4bb] Question about P3, H3 and R3 space groups

[Ian Tickle]

The important take-home message in this excellent article is surely the
conclusion:

"The significant amount of programming effort and user frustration caused
by the H3 and H32 space-group symbols is a good example of how time can be
lost by not adopting long-established standards.  This is not meant to
suggest revising the PDB as this would certainly only serve to increase the
confusion.  Rather, it is a salient reminder to the entire crystallographic
methods-developer community to avoid ad-hoc approaches whenever possible.
Ever more automated systems require highly reliable components and
unambiguous semantics.  The effort spent early in ensuring reliability and
clarity is usually rewarded many times over as time passes."

... and I would add adherence to established conventions.

Cheers

-- Ian


On Wed, 22 Jul 2020 at 14:42, Gildea, Richard (DLSLtd,RAL,LSCI) <
richard.gil...@diamond.ac.uk> wrote:

> 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  on behalf of David
> Vizarraga Revuelto 
> *Sent:* 22 July 2020 12:20
> *To:* 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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Re: [ccp4bb] Question about P3, H3 and R3 space groups

[LMB]

When I was writing Pointless I had to do all sorts of kludgy things to cope 
with the different “conventions” used by ccp4, clipper and cctbx libraries, 
scalepack etc.  The PDB should have stuck to established conventions to avoid 
confusion. And lots of people for some reason seem not to like space groups 
like I2 and P 2 21 21

Phil

Sent from my iPad

> On 22 Jul 2020, at 14:42, Gildea, Richard (DLSLtd,RAL,LSCI) 
>  wrote:
> 
> 
> 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  on behalf of David 
> Vizarraga Revuelto 
> Sent: 22 July 2020 12:20
> To: 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  148. R -3   155. R 3 2  160. R 3 m  161. R 3 c  
> 166. R -3 m
> 167. R -3 c
> H-centred Trigonal
> 143. H 3  144. H 31   145. H 32   147. H -3   149. H 3 2 1
> 150. H 3 1 2
> 151. H 31 2 1 152. H 31 1 2   153. H 32 2 1   154. H 32 1 2   156. H 3 1 m
> 157. H 3 m 1
> 158. H 3 1 c  159. H 3 c 1162. H -3 m 1   163. H -3 c 1   164. H -3 1 m   
> 165. H -3 1 c
> 
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>  
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Re: [ccp4bb] Question about P3, H3 and R3 space groups

[Ian Tickle]

Hi Eleanor

H3 #143 is (and always has been) a triply-primitive cell setting of P3.

http://img.chem.ucl.ac.uk/sgp/large/143bz1.htm

Cheers

-- Ian


On Wed, 22 Jul 2020 at 14:42, Eleanor Dodson <
176a9d5ebad7-dmarc-requ...@jiscmail.ac.uk> wrote:

> But surely P3 symmetry ' cell ( a,a,c 90 90 120) with origin shifts
> (⅓,⅔,0), +(⅔,⅓,0) can just be indexed as P3 with
> cell (a/sqrt(3), a/sqrt(3), c, 90 90 120) ??
> Eleanor
>
> On Wed, 22 Jul 2020 at 14:32, Nicholas Keep 
> wrote:
>
>> I have an answer from Jeremy Cockcroft the author of the 'Birkbeck'
>> Tables. Actually Jeremy has been at UCL for a decade or so and they are
>> hosted from their
>>
>> Nick
>>
>> In answer to the question regarding the use of R and H for trigonal space
>> groups, the letters refer to two distinct types of lattice centring
>> symmetry operation, namely +(⅓,⅔,⅔), +(⅔,⅓,⅓) and +(⅓,⅔,0), +(⅔,⅓,0),
>> respectively. For the subset of rhombohedral space groups, the symbol R
>> should always be used.  When the alternative unit cell with a=b=c and
>> α=β=γ is chosen, this cell corresponds to a primitive Bravais lattice, but
>> the label P is not used as this would result in confusion with
>> non-rhombohedral space groups.  (The choice of symmetry operators for
>> rhombohedral space groups is wholly dependent of the choice of unit cell,
>> i.e. hexagonal versus rhombohedral, so there is no ambiguity if the unit
>> cell is specified.)
>>
>> For the non-rhombohedral space groups, it may occasionally be convenient
>> to choose a larger H-centred unit cell that is not the usual primitive P
>> one.  (The use of larger unit cells is quite common for systems that
>> undergo phase transformations as it may enable the crystallographer to keep
>> the contents of the unit cell the same in both phases.)  Note that the
>> use of an H-centred lattice switches the order of the symmetry elements in
>> these space group symbols, e.g. P312 becomes H321.
>>
>> I am not aware of any changes to this convention, which I believe has a
>> long history.  However, it is possible that the letter H has been used
>> unwittingly for other purposes.
>>
>> Jeremy Karl Cockcroft
>>
>>
>> --
>>
>> NOTE NEW PHONE NUMBER JULY 2020
>>
>> Prof Nicholas H. Keep
>> Executive Dean of School of Science
>> Professor of Biomolecular Science
>> Crystallography, Institute for Structural and Molecular Biology,
>> Department of Biological Sciences
>> Birkbeck,  University of London,
>> Malet Street,
>> Bloomsbury
>> LONDON
>> WC1E 7HX
>>
>> Office G54a
>>
>> Dean Email;  scid...@bbk.ac.uk
>> Dept email n.k...@mail.cryst.bbk.ac.uk
>> Telephone 020-3926-3475  (Will contact me at home if working as well as my 
>> office)
>>
>> If you want to access me in person you have to come to the crystallography 
>> entrance
>> and ring me or the department office from the internal phone by the door
>>
>>
>> --
>>
>> To unsubscribe from the CCP4BB list, click the following link:
>> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1
>>
>
> --
>
> To unsubscribe from the CCP4BB list, click the following link:
> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1
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Re: [ccp4bb] Question about P3, H3 and R3 space groups

[Eleanor Dodson]

But surely P3 symmetry ' cell ( a,a,c 90 90 120) with origin shifts
(⅓,⅔,0), +(⅔,⅓,0) can just be indexed as P3 with
cell (a/sqrt(3), a/sqrt(3), c, 90 90 120) ??
Eleanor

On Wed, 22 Jul 2020 at 14:32, Nicholas Keep 
wrote:

> I have an answer from Jeremy Cockcroft the author of the 'Birkbeck'
> Tables. Actually Jeremy has been at UCL for a decade or so and they are
> hosted from their
>
> Nick
>
> In answer to the question regarding the use of R and H for trigonal space
> groups, the letters refer to two distinct types of lattice centring
> symmetry operation, namely +(⅓,⅔,⅔), +(⅔,⅓,⅓) and +(⅓,⅔,0), +(⅔,⅓,0),
> respectively. For the subset of rhombohedral space groups, the symbol R
> should always be used.  When the alternative unit cell with a=b=c and
> α=β=γ is chosen, this cell corresponds to a primitive Bravais lattice, but
> the label P is not used as this would result in confusion with
> non-rhombohedral space groups.  (The choice of symmetry operators for
> rhombohedral space groups is wholly dependent of the choice of unit cell,
> i.e. hexagonal versus rhombohedral, so there is no ambiguity if the unit
> cell is specified.)
>
> For the non-rhombohedral space groups, it may occasionally be convenient
> to choose a larger H-centred unit cell that is not the usual primitive P
> one.  (The use of larger unit cells is quite common for systems that
> undergo phase transformations as it may enable the crystallographer to keep
> the contents of the unit cell the same in both phases.)  Note that the
> use of an H-centred lattice switches the order of the symmetry elements in
> these space group symbols, e.g. P312 becomes H321.
>
> I am not aware of any changes to this convention, which I believe has a
> long history.  However, it is possible that the letter H has been used
> unwittingly for other purposes.
>
> Jeremy Karl Cockcroft
>
>
> --
>
> NOTE NEW PHONE NUMBER JULY 2020
>
> Prof Nicholas H. Keep
> Executive Dean of School of Science
> Professor of Biomolecular Science
> Crystallography, Institute for Structural and Molecular Biology,
> Department of Biological Sciences
> Birkbeck,  University of London,
> Malet Street,
> Bloomsbury
> LONDON
> WC1E 7HX
>
> Office G54a
>
> Dean Email;   scid...@bbk.ac.uk
> Dept email n.k...@mail.cryst.bbk.ac.uk
> Telephone 020-3926-3475  (Will contact me at home if working as well as my 
> office)
>
> If you want to access me in person you have to come to the crystallography 
> entrance
> and ring me or the department office from the internal phone by the door
>
>
> --
>
> To unsubscribe from the CCP4BB list, click the following link:
> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1
>



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Re: [ccp4bb] Question about P3, H3 and R3 space groups

[Gildea, Richard (DLSLtd,RAL,LSCI)]

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  on behalf of David Vizarraga 
Revuelto 
Sent: 22 July 2020 12:20
To: 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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please notify us of receipt by returning the e-mail and do not use, copy, 
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the message.
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Wales with its registered office at Diamond House, Harwell Science and 
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[ccp4bb] Question about P3, H3 and R3 space groups

[Nicholas Keep]

I have an answer from Jeremy Cockcroft the author of the 'Birkbeck' 
Tables. Actually Jeremy has been at UCL for a decade or so and they are 
hosted from their


Nick

In answer to the question regarding the use of R and H for trigonal 
space groups, the letters refer to two distinct types of lattice 
centring symmetry operation, namely +(⅓,⅔,⅔), +(⅔,⅓,⅓) and +(⅓,⅔,0), 
+(⅔,⅓,0), respectively. For the subset of rhombohedral space groups, the 
symbol R should always be used.When the alternative unit cell with a=b=c 
and α=β=γ is chosen, this cell corresponds to a primitive Bravais 
lattice, but the label P is not used as this would result in confusion 
with non-rhombohedral space groups. (The choice of symmetry operators 
for rhombohedral space groups is wholly dependent of the choice of unit 
cell, i.e. hexagonal versus rhombohedral, so there is no ambiguity if 
the unit cell is specified.)


For the non-rhombohedral space groups, it may occasionally be convenient 
to choose a larger H-centred unit cell that is not the usual primitive P 
one.(The use of larger unit cells is quite common for systems that 
undergo phase transformations as it may enable the crystallographer to 
keep the contents of the unit cell the same in both phases.)Note that 
the use of an H-centred lattice switches the order of the symmetry 
elements in these space group symbols, e.g. P312 becomes H321.


I am not aware of any changes to this convention, which I believe has a 
long history. However, it is possible that the letter H has been used 
unwittingly for other purposes.


Jeremy Karl Cockcroft


--

NOTE NEW PHONE NUMBER JULY 2020

Prof Nicholas H. Keep
Executive Dean of School of Science
Professor of Biomolecular Science
Crystallography, Institute for Structural and Molecular Biology,
Department of Biological Sciences
Birkbeck,  University of London,
Malet Street,
Bloomsbury
LONDON
WC1E 7HX

Office G54a

Dean Email; scid...@bbk.ac.uk
Dept email n.k...@mail.cryst.bbk.ac.uk
Telephone 020-3926-3475  (Will contact me at home if working as well as my 
office)

If you want to access me in person you have to come to the crystallography 
entrance
and ring me or the department office from the internal phone by the door




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Re: [ccp4bb] Question about P3, H3 and R3 space groups

[George Sheldrick]

This is precisely why SHELX always used the coordinates of the general 
position (LATT+SYMM) to define the space group rather than a name or number.


George

On 22/07/20 14:15, Ian Tickle wrote:


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 
mailto: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    148.
/R/ -3    155.
/R/ 3 2   160.
/R/ 3 /m/ 161.
/R/ 3 /c/ 166.
/R/ -3 /m/ 
167. /R/ -3 /c/ 
  
H-centred Trigonal
143. /H/ 3    144.
/H/ 3_1   145.
/H/ 3_2   147.
/H/ -3    149.
/H/ 3 2 1 150.
/H/ 3 1 2 
151. /H/ 3_1  2 1 
152. /H/ 3_1  1 2
  153. /H/ 3_2  2
1 154. /H/ 3_2
 1 2  156. /H/ 3
1 /m/ 157. /H/ 3
/m/ 1 
158. /H/ 3 1 /c/ 
159. /H/ 3 /c/ 1 
162. /H/ -3 /m/ 1 
163. /H/ -3 /c/ 1
  164. /H/ -3 1
/m/   165.
/H/ -3 1 /c/ 




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This message was

Re: [ccp4bb] Question about P3, H3 and R3 space groups

[Ian Tickle]

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 
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  148. *R* -3
>  155. *R* 3 2
>  160. *R* 3 *m*
>  161. *R* 3 *c*
>  166. *R* -3 *m*
> 
> 167. *R* -3 *c* 
> H-centred Trigonal
> 143. *H* 3  144. *H* 31
>  145. *H* 32
>  147. *H* -3
>  149. *H* 3 2 1
>  150. *H* 3 1 2
> 
> 151. *H* 31 2 1  152. *H*
>  31 1 2  153. *H* 32 2 1
>  154. *H* 32 1 2
>  156. *H* 3 1 *m*
>  157. *H* 3 *m* 1
> 
> 158. *H* 3 1 *c*  159. *H*
>  3 *c* 1  162. *H* -3 *m*
>  1  163. *H* -3 *c* 1
>  164. *H* -3 1 *m*
>  165. *H* -3 1 *c*
> 
>
> --
>
> To unsubscribe from the CCP4BB list, click the following link:
> https://www.jiscmail.ac.uk/cgi-bin/WA-JISC.exe?SUBED1=CCP4BB&A=1
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Re: [ccp4bb] Question about P3, H3 and R3 space groups

[Eleanor Dodson]

This does seem confusing!
Maybe the International tables have changed, but in my copy spacegroup 143
is labelled P3

Spacegroup 146 is equivalent to P3 with translations 1/3,2/3.2/3  and
2/3,1/3,1/3 is called rhombehedral
This can be indexed with.  "a=b=c in the rhombehedral setting" and labelled
R3, but it is usually and more conveniently indexed in " the hexagonal
setting with a=b, and gamma = 120", and with the translations to alternate
origins 1/3,2/3.2/3  and 2/3,1/3,1/3 labeled R 3:H
See this  extract from $CLIBD/syminfo.lib

  begin_spacegroup

number  146

basisop x,y,z

symbol ccp4 146

symbol Hall ' R 3'

symbol xHM  'R 3 :H'

symbol old  'H 3'

symbol laue '-P 3' '-3'

symbol patt '-R 3' '-3'

symbol pgrp ' P 3' '3'

hklasu ccp4 '(h>=0 and k>0) or (h=0 and k=0 and l>=0)'

mapasu ccp4 0<=x<=2/3; 0<=y<=2/3; 0<=z<1/3

mapasu zero 0<=x<=1/3; 0<=y<=1/3; 0<=z<1

mapasu nonz 0<=x<=1/3; 0<=y<=1/3; 0<=z<1

cheshire 0<=x<=2/3; 0<=y<=2/3; 0<=z<=0

symop x,y,z

symop -y,x-y,z

symop -x+y,-x,z

cenop x,y,z

cenop x+2/3,y+1/3,z+1/3

cenop x+1/3,y+2/3,z+2/3

end_spacegroup

On Wed, 22 Jul 2020 at 12:32, David Vizarraga Revuelto 
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  148. *R* -3
>  155. *R* 3 2
>  160. *R* 3 *m*
>  161. *R* 3 *c*
>  166. *R* -3 *m*
> 
> 167. *R* -3 *c* 
> H-centred Trigonal
> 143. *H* 3  144. *H* 31
>  145. *H* 32
>  147. *H* -3
>  149. *H* 3 2 1
>  150. *H* 3 1 2
> 
> 151. *H* 31 2 1  152. *H*
>  31 1 2  153. *H* 32 2 1
>  154. *H* 32 1 2
>  156. *H* 3 1 *m*
>  157. *H* 3 *m* 1
> 
> 158. *H* 3 1 *c*  159. *H*
>  3 *c* 1  162. *H* -3 *m*
>  1  163. *H* -3 *c* 1
>  164. *H* -3 1 *m*
>  165. *H* -3 1 *c*
> 
>
> --
>
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[ccp4bb] Question about P3, H3 and R3 space groups

[David Vizarraga Revuelto]

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  148. *R* -3
 155. *R* 3 2
 160. *R* 3 *m*
 161. *R* 3 *c*
 166. *R* -3 *m*

167. *R* -3 *c* 
H-centred Trigonal
143. *H* 3  144. *H* 31
 145. *H* 32
 147. *H* -3
 149. *H* 3 2 1
 150. *H* 3 1 2

151. *H* 31 2 1  152. *H* 31
 1 2  153. *H* 32 2 1
 154. *H* 32 1 2
 156. *H* 3 1 *m*
 157. *H* 3 *m* 1

158. *H* 3 1 *c*  159. *H*
 3 *c* 1  162. *H* -3 *m* 1
 163. *H* -3 *c* 1
 164. *H* -3 1 *m*
 165. *H* -3 1 *c*




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