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From: peter murrayrust <pm286@ca...>  20060906 07:28:09

At 03:48 06/09/2006, Bob Hanson wrote: >Egon and Nico and others  > >I'm quite excited about this space group business and Jmol. So am I. >Probably >some of these methods should be ported to the CDK, as they will have >quite general interest. Certainly. In fact I think this should be done as a general Blue Obelisk resource as it's so important. Other wise we run the risk of different variant implementations in Jmol, CDK, JUMBO, Openbabel, etc. It doesn't really alter the work to be done, simply how it is packaged. So if we have, say, BOSG (Blue Obelisk Space Groups) then it could comprise: * definitive and tutorial material * lookup tables (e.g. for HM> Hall) * Hall2SymOp generating code. This might have to be ported to C++ as well and possibly also FORTRAN for The solid state community * other utility routines. This has the advantage that the information is only held once so that bugs in lookup table are mended for everyone simultaneously >The three classes are: > > HallInfo  parses and inteprets Hall symbols, > generating the associated matrices > > SymmetryOperation  extends Matrix4f; parses and > generates "x,y,z" lists and matrices Note that the use of x/12 is restricted to crystallography. In principle the matrix translations elements can be anything (although they won't generate a spacegroup). The spacegroup is generated by applying an infinite number of translation matrixes to the spacegroup type. I can see that Hall matrices could be used for lower dimensionality problems (e.g. surfaces and fibres) where some of the periodic translations are omitted. This is why CML uses real numbers in the 4*4 matrices > SpaceGroup  overall container for a space group; > generates full operation list; looks up > symbol names; identifies unique axis; This is formally a spacegroup type, I think > does the actual atom coordinate operations > The atom coordinate operations require knowledge of the structure and that can be held in many ways. It might apply when there is a clear externalized data structure like CIF or CML. But there is also the problem of how the periodic translations are actually applied so I would omit this operation. >Q: Do you think we should set it up so that the list of 600+ space >groups is read by Jmol from an external source only if/when it needs it? Yes. (I would prefer to see Jmol us a BO spacegroup routine for this purpose) >Q: What's the proper way to do that  would it be included in the >distribution as a TXT file? It can be held in CML iif this is useful. It can probably also be held in CIF with implicit semantics. I don't like TXT files if they can be avoided >Q: Would Jmol read this automatically when it needed to? Or would we >have some sort of DATA command that might read other data types as well. >(Color schemes?) Or might we just set it up as a script file and use the >mechanism already in place  something like: This is a general Jmol question  I would prefer to see as much generic functionality as possible normalised in BO resources as: * it avoids multiple sources (e.g. we should only have one periodic table within all BO software. That is certainly my intention for JUMBO, though I haven't actually done it. It makes things like covalent radii much more normalised * we use the same algorithms for bonding, bond orders, etc. So if atoms are bonded by default in Jmol then they should be in JUMBO and CDK * we use the same colour schemes etc. etc. Jmol has done massive work in this area and there is a lot in there that we can benefit from. As you know we are meeting in SF next week. Christoph will not be drinking beer... >#_data spacegroup >.... >.... >.... >#_end data > >so that it all can be in a script file? > >Syd, what do you know about the format of this sort of data? Do other >programs read that data in a standard format? Perhaps XML? There is a lot of similar stuff in solid state programs, especially GULP, CASTEP< SIESTA< DL_POLY, etc. There would be a great advantage to having symmetry normalised across them. I don't think it's difficult P. Peter MurrayRust Unilever Centre for Molecular Sciences Informatics University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK +441223763069 
From: Bob Hanson <hansonr@st...>  20060906 02:48:38

Egon and Nico and others  I'm quite excited about this space group business and Jmol. Probably some of these methods should be ported to the CDK, as they will have quite general interest. The three classes are: HallInfo  parses and inteprets Hall symbols, generating the associated matrices SymmetryOperation  extends Matrix4f; parses and generates "x,y,z" lists and matrices SpaceGroup  overall container for a space group; generates full operation list; looks up symbol names; identifies unique axis; does the actual atom coordinate operations Q: Do you think we should set it up so that the list of 600+ space groups is read by Jmol from an external source only if/when it needs it? Q: What's the proper way to do that  would it be included in the distribution as a TXT file? Q: Would Jmol read this automatically when it needed to? Or would we have some sort of DATA command that might read other data types as well. (Color schemes?) Or might we just set it up as a script file and use the mechanism already in place  something like: #_data spacegroup .... .... .... #_end data so that it all can be in a script file? Syd, what do you know about the format of this sort of data? Do other programs read that data in a standard format? Perhaps XML? Bob  Original Message  Subject: Re: [Fwd: Re: Space Groups] Date: Wed, 6 Sep 2006 09:44:08 +0800 From: Sydney Hall <syd@...> To: Bob Hanson <hansonr@...> CC: peter murrayrust <pm286@...> References: <44FBF973.1070909@...> <4E04055D11BD4A498E85937CE8F2251F@...> <44FCE597.6030400@...> Hi Bob and Peter. Ta for the communications. I'll give you a more detailed response tomorrow when I'm in the lab again. I'm only an occasional academic these days and at the moment most of that time is taken up with the development of a new ddl for the IUCr (Peter knows about this from Florence). Two quick observations for the moment. > Oh, yes. This is fabulous. In intriguing idea occurs to me. We > could make this totally general and totally customizable  Your > file is in CIF format. How about if Jmol has none of this hardwired >  or maybe some defaults hardwired  but allows reading of this > CIF file as a replacement/supplement? So then anyone could expand > this as desired. If it's a living document, then the update to Jmol > would then just be the replacement of this file in come common > directory on a user's system. I savvy crystallographer could > augment it as desired. We always externalise this sort of information from your software where we can. Makes it simple to update and easy for users to understand. We recommend the same approach be applied to validation tests and to the use of cif dictionaries  early browsers internalised the dictionary definitions and ignored the dynamic nature of these entries! :( > rotation term 1 > input code: 4n; primitive code: 4zn > order: 4; axisType: z; translation: n > operator: y+1/2,x+1/2,z+1/2 > Seitz matrix(12ths): [ > [0.0 1.0 0.0 6.0] > [1.0 0.0 0.0 6.0] > [0.0 0.0 1.0 6.0] > [0.0 0.0 0.0 1.0] ] A small and obvious point on the above... only the translation elements in your Seitz matrix are in 12ths. In matrices generated by SYMGEN all elements are in 12ths  so its best to make this point clear in your output... to avoid temporary puzzlement! :) More later. Cheers Syd PS: Peter, how did that paper you were writing at Florence on "methods in schema" go? This may be relevant to our current prognostications.  Emeritus Professor Syd Hall School Biomedical, Biomolecular & Chemical Sciences University of Western Australia Crawley, 6009 AUSTRALIA. Ph: +61 (8) 6488 2725 On 05/09/2006, at 10:48 AM, Bob Hanson wrote: > Dear Syd, > > Thanks for the quick reply. I have this working now, and I will > implement the nonstandard issues. I'm delighted that you are > available to work with us on this. Already I can see that this will > be a welcome addition. I've put in a mechanism to allow for either > reading the explicit operators listed in a CIF file or ignore them, > and already I've had a surprise or two. More on that after > interspersed comments below. I've CCed Peter on this because I'm > sure he will be at least as interested as I in your comments. > > Sydney Hall wrote: > > >> Dear Bob >> >> This notation should be a useful addition to Jmol if only >> to provide some origin specificity for nonconventional >> space groups. I will help you with this where I can. >> >> >>> >>> 2. the second rotation (if N is 2) has an axis direction of >>>  a if preceded by an N of 2 or 4 >>>  *a+b* if preceded by an N of 3 or 6 >>> >>> Should this read "ab" rather than "a+b" in that second case? It >>> seems to me that what is intended is that the space group <P 3 >>> 2> is explicity <P 3z 2'> not <P 3z 2">, and 2' is ab, not a+b. >>> >> >> >> Indeed it should be "ab" in this case, and the second edition >> of International Tables Vol B (2001) has corrected this error. I >> hadn't appreciated until your mail that this old typo still exists >> on Ralf's website! I will contact him today and get it fixed. >> >> >>> 2. In the discussion of Table 4: based on the included list of >>> space groups, which I presume to be complete, it would appear >>> that it is not possible to have 2' or 2" when the preceding axis >>> is NOT Nz. I wonder why there is the discussion there of Nx and >>> Ny in relation to 2' and 2". Is that necessary? >>> >> >> >> The notation is kept as general as possible. There is no obligation >> in trigonal/hexagonal space groups to place a 3/6 fold rotation >> along z >> though it is the usual convention. In some phase transition >> problems it >> is highly desirable to use nonconventional axial settings. >> >> > The Nx and Ny possibilities are implmented. Unfortunately I don't > see an easy way of clearly specifying them in notational form (just > for lookup purposes) other than this implicit dependence on the > previous rotational direction, but I can manage. > > >>> 3. I guess my main question relates to the general >>> implementation of Hall symbols. Is it intended that there be >>> exactly one Hall symbol for each possible space group >>> possibility? That is, are there exactly 530 legitimate Hall >>> symbols? Or is it conceivable/ appropriate for people to invent >>> their own equivalent set of Hall symbols for any given space group? >>> >> >> >> This notation is not intended as a static space group identifier >> in the >> sense that the HM symbols are. It simply identifies the generator >> Sietz >> matrices and as such is a general representation for any space group >> symmetry in any axial or origin setting. It provides an exact >> computat >> ional approach. The HM symbols are not general and are imprecise >> computationally. By their very nature, several Hall representations >> (using a different choice of generator matrices) can generate the >> same >> space group symmetry though there are some conventions that avoid >> this >> being a distraction (computationally all representations are >> equivalent). >> >> I would recommend therefore that you treat the symmetry generation >> for >> this approach in a completely general way. The table shown on Ralf's >> website (and in Volume B) is intended really for mapping HM >> symbols to >> Hall symbols rather than the reverse. It is used extensively in >> the Acta >> validation software (e.g. CIFCHECK) so that space group equivalent >> positions can be easily generated and checked against those >> submitted. >> As you will appreciate generating ep's from the generator matrices is >> trivial and building the Hall notation from the ep's is not >> difficult. >> >> > Right, Except for (nx ny nz), which I only implemented as (0 0 nz) > today  but will fix momentarily  I think I have all the > conversions in. I realize that many data files use the Hermann > Mauguin symbols and not Hall, so there's still a need to translate > those. I suppose there is just going to have to be some flexibility/ > ambiguity there. Jmol is programmed to read explicit operator > listings in CIF and RES files, so provided those are there, there > will be no problem. The problem will only be if someone is reading > a file with just the HM symbol and using unspecified origin and > such. Part of what I was interested in as well was allowing for > what I am calling "abbreviated HM symbols"  the sorts of things > you see in older references  "P 2/1" insead of "P 1 2/1 1", for > instance. Jmol can find the unique axis and do the proper correlation. > > > >> I have attached a more recent version of the space group mapping file >> than that on Ralf's website (this matches the one in the 2001 >> edition of >> IT Vol C). Both are correct but the latest version uses the more >> "conventional" representations that appear in Acta and most CIF's. >> >> Hope this helps.... good luck with the implementation. Let me know >> if I can help in any other respect. >> >> > Oh, yes. This is fabulous. In intriguing idea occurs to me. We > could make this totally general and totally customizable  Your > file is in CIF format. How about if Jmol has none of this hardwired >  or maybe some defaults hardwired  but allows reading of this > CIF file as a replacement/supplement? So then anyone could expand > this as desired. If it's a living document, then the update to Jmol > would then just be the replacement of this file in come common > directory on a user's system. I savvy crystallographer could > augment it as desired. > > I think the best thing at this point is for me to let others > suggest how they want it implemented. I'll send a message to users > and also CC you, Syd. > > I have a small number of additional question but will get this > initial implementation in first so you can take a look yourself and > offer suggestions. > > OK, here was my first surprise: http://www.stolaf.edu/academics/ > chemapps/jmol/docs/examples11/data/quartz.cif curiously enough > does not have enough information in the naming and cell parameters > to generate the given operators correctly. The HM symbol given in > that CIF file is <P 32 2 1> (#154). When I look that up, I see <P > 32 2">. This is also what the cctbk explore_symmetry page gives. > But to get the same list of operators as in the CIF file, I have to > use <P 32 2" (0 0 4)>. So I'm wondering if that is a general > problem  that conversions from (HM+cell parameters) to (Hall) is > inherently ambiguous, and it is just basically impossible to use a > HM symbol to generate the operators. Or, perhaps there is an error > in this CIF file. What do you think? > > > Bob > > > >> Cheers >> Syd >>  >> Emeritus Professor Sydney R. Hall >> School Biomedical, Biomolecular & Chemical Sciences >> University of Western Australia >> Crawley, 6009 AUSTRALIA. >> Ph: +61 (8) 6488 2725 >> >>  >>  >> >> # >> # hall symmetry notation >> # >> # table of ralf w. grossekunstleve, eth, zuerich. >> # >> # version june 1995 >> # updated september 29 1995 >> # updated july 9 1997 >> # updated july 24 1998 >> # last updated june 11 2000 >> >> data_notation >> >> loop_ >> _monoclinic_extension # cf. _symmetry_space_group_id >> _monoclinic_axis # cf. it vol. a 1983 sec. 2.16. >> _monoclinic_setting # cf. it vol. a 1983 tab. 2.16.1. >> _monoclinic_cellchoice # cf. it vol. a 1983 sec. 2.16.(i) & >> fig. 2.6.4. >> >> b b abc 1 >> b1 b abc 1 >> b2 b abc 2 >> b3 b abc 3 >> b b cba 1 >> b1 b cba 1 >> b2 b cba 2 >> b3 b cba 3 >> c c abc 1 >> c1 c abc 1 >> c2 c abc 2 >> c3 c abc 3 >> c c bac 1 >> c1 c bac 1 >> c2 c bac 2 >> c3 c bac 3 >> a a abc 1 >> a1 a abc 1 >> a2 a abc 2 >> a3 a abc 3 >> a a acb 1 >> a1 a acb 1 >> a2 a acb 2 >> a3 a acb 3 >> >> >> loop_ >> _symmetry_space_group_id >> _symmetry_space_group_name_sch >> _symmetry_space_group_name_hm # recognised iucr cif data names >> _symmetry_space_group_name_hall # recognised iucr cif data names >> >> 1 c1^1 p_1 p_1 2 >> ci^1 p_1 p_1 3:b c2^1 >> p_1_2_1 p_2y 3:b c2^1 p_2 >> p_2y 3:c c2^1 p_1_1_2 >> p_2 3:a c2^1 p_2_1_1 >> p_2x 4:b c2^2 p_1_21_1 >> p_2yb 4:b c2^2 p_1_21_1 p_2y1 >> 4:b c2^2 p_21 p_2yb 4:c >> c2^2 p_1_1_21 p_2c 4:c c2^2 >> p_1_1_21 p_21 4:a c2^2 p_21_1_1 >> p_2xa 4:a c2^2 p_21_1_1 p_2x1 >> 5:b1 c2^3 c_1_2_1 c_2y 5:b1 >> c2^3 c_2 c_2y 5:b2 c2^3 >> a_1_2_1 a_2y 5:b3 c2^3 i_1_2_1 >> i_2y 5:c1 c2^3 a_1_1_2 >> a_2 5:c2 c2^3 b_1_1_2 >> b_2 5:c3 c2^3 i_1_1_2 >> i_2 5:a1 c2^3 b_2_1_1 >> b_2x 5:a2 c2^3 c_2_1_1 >> c_2x 5:a3 c2^3 i_2_1_1 >> i_2x 6:b cs^1 p_1_m_1 >> p_2y 6:b cs^1 p_m >> p_2y 6:c cs^1 p_1_1_m >> p_2 6:a cs^1 p_m_1_1 >> p_2x 7:b1 cs^2 p_1_c_1 >> p_2yc 7:b1 cs^2 p_c >> p_2yc 7:b2 cs^2 p_1_n_1 >> p_2yac 7:b2 cs^2 p_n >> p_2yac 7:b3 cs^2 p_1_a_1 >> p_2ya 7:b3 cs^2 p_a >> p_2ya 7:c1 cs^2 p_1_1_a >> p_2a 7:c2 cs^2 p_1_1_n >> p_2ab 7:c3 cs^2 p_1_1_b >> p_2b 7:a1 cs^2 p_b_1_1 >> p_2xb 7:a2 cs^2 p_n_1_1 >> p_2xbc 7:a3 cs^2 p_c_1_1 >> p_2xc 8:b1 cs^3 c_1_m_1 >> c_2y 8:b1 cs^3 c_m >> c_2y 8:b2 cs^3 a_1_m_1 >> a_2y 8:b3 cs^3 i_1_m_1 >> i_2y 8:b3 cs^3 i_m >> i_2y 8:c1 cs^3 a_1_1_m >> a_2 8:c2 cs^3 b_1_1_m >> b_2 8:c3 cs^3 i_1_1_m >> i_2 8:a1 cs^3 b_m_1_1 >> b_2x 8:a2 cs^3 c_m_1_1 >> c_2x 8:a3 cs^3 i_m_1_1 >> i_2x 9:b1 cs^4 c_1_c_1 >> c_2yc 9:b1 cs^4 c_c >> c_2yc 9:b2 cs^4 a_1_n_1 a_2yab >> # a_2yac 9:b3 cs^4 i_1_a_1 >> i_2ya 9:b1 cs^4 a_1_a_1 >> a_2ya 9:b2 cs^4 c_1_n_1 c_2yac >> # c_2ybc 9:b3 cs^4 i_1_c_1 >> i_2yc 9:c1 cs^4 a_1_1_a >> a_2a 9:c2 cs^4 b_1_1_n b_2ab >> # b_2bc 9:c3 cs^4 i_1_1_b >> i_2b 9:c1 cs^4 b_1_1_b >> b_2b 9:c2 cs^4 a_1_1_n a_2ab >> # a_2ac 9:c3 cs^4 i_1_1_a >> i_2a 9:a1 cs^4 b_b_1_1 >> b_2xb 9:a2 cs^4 c_n_1_1 c_2xac >> # c_2xbc 9:a3 cs^4 i_c_1_1 i_2xc >> 9:a1 cs^4 c_c_1_1 c_2xc 9:a2 >> cs^4 b_n_1_1 b_2xab # b_2xbc >> 9:a3 cs^4 i_b_1_1 i_2xb 10:b >> c2h^1 p_1_2/m_1 p_2y 10:b c2h^1 p_2/ >> m p_2y 10:c c2h^1 p_1_1_2/m  >> p_2 10:a c2h^1 p_2/m_1_1  >> p_2x 11:b c2h^2 p_1_21/m_1  >> p_2yb 11:b c2h^2 p_1_21/m_1 p_2y1 >> 11:b c2h^2 p_21/m p_2yb 11:c >> c2h^2 p_1_1_21/m p_2c 11:c c2h^2 >> p_1_1_21/m p_21 11:a c2h^2 p_21/m_1_1  >> p_2xa 11:a c2h^2 p_21/m_1_1 p_2x1 >> 12:b1 c2h^3 c_1_2/m_1 c_2y 12:b1 >> c2h^3 c_2/m c_2y 12:b2 c2h^3 a_1_2/ >> m_1 a_2y 12:b3 c2h^3 i_1_2/m_1  >> i_2y 12:b3 c2h^3 i_2/m  >> i_2y 12:c1 c2h^3 a_1_1_2/m  >> a_2 12:c2 c2h^3 b_1_1_2/m  >> b_2 12:c3 c2h^3 i_1_1_2/m  >> i_2 12:a1 c2h^3 b_2/m_1_1  >> b_2x 12:a2 c2h^3 c_2/m_1_1  >> c_2x 12:a3 c2h^3 i_2/m_1_1  >> i_2x 13:b1 c2h^4 p_1_2/c_1  >> p_2yc 13:b1 c2h^4 p_2/c  >> p_2yc 13:b2 c2h^4 p_1_2/n_1  >> p_2yac 13:b2 c2h^4 p_2/n  >> p_2yac 13:b3 c2h^4 p_1_2/a_1  >> p_2ya 13:b3 c2h^4 p_2/a  >> p_2ya 13:c1 c2h^4 p_1_1_2/a  >> p_2a 13:c2 c2h^4 p_1_1_2/n  >> p_2ab 13:c3 c2h^4 p_1_1_2/b  >> p_2b 13:a1 c2h^4 p_2/b_1_1  >> p_2xb 13:a2 c2h^4 p_2/n_1_1  >> p_2xbc 13:a3 c2h^4 p_2/c_1_1  >> p_2xc 14:b1 c2h^5 p_1_21/c_1  >> p_2ybc 14:b1 c2h^5 p_21/c  >> p_2ybc 14:b2 c2h^5 p_1_21/n_1  >> p_2yn 14:b2 c2h^5 p_21/n  >> p_2yn 14:b3 c2h^5 p_1_21/a_1  >> p_2yab 14:b3 c2h^5 p_21/a  >> p_2yab 14:c1 c2h^5 p_1_1_21/a  >> p_2ac 14:c2 c2h^5 p_1_1_21/n  >> p_2n 14:c3 c2h^5 p_1_1_21/b  >> p_2bc 14:a1 c2h^5 p_21/b_1_1  >> p_2xab 14:a2 c2h^5 p_21/n_1_1  >> p_2xn 14:a3 c2h^5 p_21/c_1_1  >> p_2xac 15:b1 c2h^6 c_1_2/c_1  >> c_2yc 15:b1 c2h^6 c_2/c  >> c_2yc 15:b2 c2h^6 a_1_2/n_1 a_2yab >> # a_2yac 15:b3 c2h^6 i_1_2/a_1  >> i_2ya 15:b3 c2h^6 i_2/a  >> i_2ya 15:b1 c2h^6 a_1_2/a_1  >> a_2ya 15:b2 c2h^6 c_1_2/n_1 c_2yac >> # c_2ybc 15:b2 c2h^6 c_2/n c_2yac #  >> c_2ybc 15:b3 c2h^6 i_1_2/c_1 i_2yc >> 15:b3 c2h^6 i_2/c i_2yc 15:c1 >> c2h^6 a_1_1_2/a a_2a 15:c2 c2h^6 >> b_1_1_2/n b_2ab # b_2bc 15:c3 c2h^6 >> i_1_1_2/b i_2b 15:c1 c2h^6 b_1_1_2/b  >> b_2b 15:c2 c2h^6 a_1_1_2/n a_2ab >> # a_2ac 15:c3 c2h^6 i_1_1_2/a i_2a >> 15:a1 c2h^6 b_2/b_1_1 b_2xb 15:a2 >> c2h^6 c_2/n_1_1 c_2xac # c_2xbc 15:a3 >> c2h^6 i_2/c_1_1 i_2xc 15:a1 c2h^6 c_2/ >> c_1_1 c_2xc 15:a2 c2h^6 b_2/n_1_1  >> b_2xab # b_2xbc 15:a3 c2h^6 i_2/b_1_1  >> i_2xb 16 d2^1 p_2_2_2 >> p_2_2 17 d2^2 p_2_2_21 >> p_2c_2 17 d2^2 p_2_2_21 p_21_2 >> 17:cab d2^2 p_21_2_2 p_2a_2a 17:bca >> d2^2 p_2_21_2 p_2_2b 18 d2^3 >> p_21_21_2 p_2_2ab 18:cab d2^3 p_2_21_21 >> p_2bc_2 18:bca d2^3 p_21_2_21 >> p_2ac_2ac 19 d2^4 p_21_21_21 >> p_2ac_2ab 20 d2^5 c_2_2_21 >> c_2c_2 20 d2^5 c_2_2_21 c_21_2 >> 20:cab d2^5 a_21_2_2 a_2a_2a 20:cab >> d2^5 a_21_2_2 a_2a_21 20:bca d2^5 b_2_21_2 >> b_2_2b 21 d2^6 c_2_2_2 >> c_2_2 21:cab d2^6 a_2_2_2 >> a_2_2 21:bca d2^6 b_2_2_2 >> b_2_2 22 d2^7 f_2_2_2 >> f_2_2 23 d2^8 i_2_2_2 >> i_2_2 24 d2^9 i_21_21_21 >> i_2b_2c 25 c2v^1 p_m_m_2 >> p_2_2 25:cab c2v^1 p_2_m_m >> p_2_2 25:bca c2v^1 p_m_2_m >> p_2_2 26 c2v^2 p_m_c_21 >> p_2c_2 26 c2v^2 p_m_c_21 p_21_2 >> 26:bac c2v^2 p_c_m_21 p_2c_2c 26:bac >> c2v^2 p_c_m_21 p_21_2c 26:cab c2v^2 p_21_m_a >> p_2a_2a 26:cba c2v^2 p_21_a_m >> p_2_2a 26:bca c2v^2 p_b_21_m >> p_2_2b 26:acb c2v^2 p_m_21_b >> p_2b_2 27 c2v^3 p_c_c_2 >> p_2_2c 27:cab c2v^3 p_2_a_a >> p_2a_2 27:bca c2v^3 p_b_2_b >> p_2b_2b 28 c2v^4 p_m_a_2 >> p_2_2a 28 c2v^4 p_m_a_2 >> p_2_21 28:bac c2v^4 p_b_m_2 >> p_2_2b 28:cab c2v^4 p_2_m_b >> p_2b_2 28:cba c2v^4 p_2_c_m >> p_2c_2 28:cba c2v^4 p_2_c_m p_21_2 >> 28:bca c2v^4 p_c_2_m p_2c_2c 28:acb >> c2v^4 p_m_2_a p_2a_2a 29 c2v^5 >> p_c_a_21 p_2c_2ac 29:bac c2v^5 p_b_c_21 >> p_2c_2b 29:cab c2v^5 p_21_a_b >> p_2b_2a 29:cba c2v^5 p_21_c_a >> p_2ac_2a 29:bca c2v^5 p_c_21_b >> p_2bc_2c 29:acb c2v^5 p_b_21_a >> p_2a_2ab 30 c2v^6 p_n_c_2 >> p_2_2bc 30:bac c2v^6 p_c_n_2 >> p_2_2ac 30:cab c2v^6 p_2_n_a >> p_2ac_2 30:cba c2v^6 p_2_a_n >> p_2ab_2 30:bca c2v^6 p_b_2_n >> p_2ab_2ab 30:acb c2v^6 p_n_2_b >> p_2bc_2bc 31 c2v^7 p_m_n_21 >> p_2ac_2 31:bac c2v^7 p_n_m_21 >> p_2bc_2bc 31:cab c2v^7 p_21_m_n >> p_2ab_2ab 31:cba c2v^7 p_21_n_m >> p_2_2ac 31:bca c2v^7 p_n_21_m >> p_2_2bc 31:acb c2v^7 p_m_21_n >> p_2ab_2 32 c2v^8 p_b_a_2 >> p_2_2ab 32:cab c2v^8 p_2_c_b >> p_2bc_2 32:bca c2v^8 p_c_2_a >> p_2ac_2ac 33 c2v^9 p_n_a_21 >> p_2c_2n 33 c2v^9 p_n_a_21 p_21_2n >> 33:bac c2v^9 p_b_n_21 p_2c_2ab 33:bac >> c2v^9 p_b_n_21 p_21_2ab 33:cab c2v^9 p_21_n_b >> p_2bc_2a 33:cab c2v^9 p_21_n_b >> p_2bc_21 33:cba c2v^9 p_21_c_n >> p_2n_2a 33:cba c2v^9 p_21_c_n >> p_2n_21 33:bca c2v^9 p_c_21_n >> p_2n_2ac 33:acb c2v^9 p_n_21_a >> p_2ac_2n 34 c2v^10 p_n_n_2 >> p_2_2n 34:cab c2v^10 p_2_n_n >> p_2n_2 34:bca c2v^10 p_n_2_n >> p_2n_2n 35 c2v^11 c_m_m_2 >> c_2_2 35:cab c2v^11 a_2_m_m >> a_2_2 35:bca c2v^11 b_m_2_m >> b_2_2 36 c2v^12 c_m_c_21 >> c_2c_2 36 c2v^12 c_m_c_21 c_21_2 >> 36:bac c2v^12 c_c_m_21 c_2c_2c 36:bac >> c2v^12 c_c_m_21 c_21_2c >> 36:cab c2v^12 a_21_m_a a_2a_2a 36:cab >> c2v^12 a_21_m_a a_2a_21 36:cba c2v^12 a_21_a_m >> a_2_2a 36:cba c2v^12 a_21_a_m a_2_21 >> 36:bca c2v^12 b_b_21_m b_2_2b 36:acb >> c2v^12 b_m_21_b b_2b_2 37 c2v^13 >> c_c_c_2 c_2_2c 37:cab c2v^13 a_2_a_a >> a_2a_2 37:bca c2v^13 b_b_2_b >> b_2b_2b 38 c2v^14 a_m_m_2 >> a_2_2 38:bac c2v^14 b_m_m_2 >> b_2_2 38:cab c2v^14 b_2_m_m >> b_2_2 38:cba c2v^14 c_2_m_m >> c_2_2 38:bca c2v^14 c_m_2_m >> c_2_2 38:acb c2v^14 a_m_2_m >> a_2_2 39 c2v^15 a_b_m_2 a_2_2b >> # a_2_2c < Jun2000 >> 39:bac c2v^15 b_m_a_2 b_2_2a # b_2_2c >> 39:cab c2v^15 b_2_c_m b_2a_2 # b_2c_2 39: >> cba c2v^15 c_2_m_b c_2a_2 # c_2b_2 39:bca >> c2v^15 c_m_2_a c_2a_2a # c_2b_2b 39:acb >> c2v^15 a_c_2_m a_2b_2b # a_2c_2c < Jun2000 >> 40 c2v^16 a_m_a_2 a_2_2a 40:bac >> c2v^16 b_b_m_2 b_2_2b 40:cab c2v^16 >> b_2_m_b b_2b_2 40:cba c2v^16 c_2_c_m >> c_2c_2 40:bca c2v^16 c_c_2_m >> c_2c_2c 40:acb c2v^16 a_m_2_a >> a_2a_2a 41 c2v^17 a_b_a_2 a_2_2ab >> # a_2_2ac 41:bac c2v^17 b_b_a_2 b_2_2ab >> # b_2_2bc >> 41:cab c2v^17 b_2_c_b b_2ab_2 # b_2bc_2 >> 41:cba c2v^17 c_2_c_b c_2ac_2 # c_2bc_2 >> 41:bca c2v^17 c_c_2_a c_2ac_2ac # c_2bc_2bc >> 41:acb c2v^17 a_c_2_a a_2ab_2ab # >> a_2ac_2ac 42 c2v^18 f_m_m_2 >> f_2_2 42:cab c2v^18 f_2_m_m >> f_2_2 42:bca c2v^18 f_m_2_m >> f_2_2 43 c2v^19 f_d_d_2 >> f_2_2d 43:cab c2v^19 f_2_d_d >> f_2d_2 43:bca c2v^19 f_d_2_d >> f_2d_2d 44 c2v^20 i_m_m_2 >> i_2_2 44:cab c2v^20 i_2_m_m >> i_2_2 44:bca c2v^20 i_m_2_m >> i_2_2 45 c2v^21 i_b_a_2 >> i_2_2c 45:cab c2v^21 i_2_c_b >> i_2a_2 45:bca c2v^21 i_c_2_a >> i_2b_2b 46 c2v^22 i_m_a_2 >> i_2_2a 46:bac c2v^22 i_b_m_2 >> i_2_2b 46:cab c2v^22 i_2_m_b >> i_2b_2 46:cba c2v^22 i_2_c_m >> i_2c_2 46:bca c2v^22 i_c_2_m >> i_2c_2c 46:acb c2v^22 i_m_2_a >> i_2a_2a 47 d2h^1 p_m_m_m  >> p_2_2 48:1 d2h^2 p_n_n_n:1 >> p_2_2_1n 48:2 d2h^2 p_n_n_n:2  >> p_2ab_2bc 49 d2h^3 p_c_c_m  >> p_2_2c 49:cab d2h^3 p_m_a_a  >> p_2a_2 49:bca d2h^3 p_b_m_b  >> p_2b_2b 50:1 d2h^4 p_b_a_n:1 >> p_2_2_1ab 50:2 d2h^4 p_b_a_n:2  >> p_2ab_2b 50:1cab d2h^4 p_n_c_b:1 >> p_2_2_1bc 50:2cab d2h^4 p_n_c_b:2  >> p_2b_2bc 50:1bca d2h^4 p_c_n_a:1 >> p_2_2_1ac 50:2bca d2h^4 p_c_n_a:2  >> p_2a_2c 51 d2h^5 p_m_m_a  >> p_2a_2a 51:bac d2h^5 p_m_m_b  >> p_2b_2 51:cab d2h^5 p_b_m_m  >> p_2_2b 51:cba d2h^5 p_c_m_m  >> p_2c_2c 51:bca d2h^5 p_m_c_m  >> p_2c_2 51:acb d2h^5 p_m_a_m  >> p_2_2a 52 d2h^6 p_n_n_a  >> p_2a_2bc 52:bac d2h^6 p_n_n_b  >> p_2b_2n 52:cab d2h^6 p_b_n_n  >> p_2n_2b 52:cba d2h^6 p_c_n_n  >> p_2ab_2c 52:bca d2h^6 p_n_c_n  >> p_2ab_2n 52:acb d2h^6 p_n_a_n  >> p_2n_2bc 53 d2h^7 p_m_n_a  >> p_2ac_2 53:bac d2h^7 p_n_m_b  >> p_2bc_2bc 53:cab d2h^7 p_b_m_n  >> p_2ab_2ab 53:cba d2h^7 p_c_n_m  >> p_2_2ac 53:bca d2h^7 p_n_c_m  >> p_2_2bc 53:acb d2h^7 p_m_a_n  >> p_2ab_2 54 d2h^8 p_c_c_a  >> p_2a_2ac 54:bac d2h^8 p_c_c_b  >> p_2b_2c 54:cab d2h^8 p_b_a_a  >> p_2a_2b 54:cba d2h^8 p_c_a_a  >> p_2ac_2c 54:bca d2h^8 p_b_c_b  >> p_2bc_2b 54:acb d2h^8 p_b_a_b  >> p_2b_2ab 55 d2h^9 p_b_a_m  >> p_2_2ab 55:cab d2h^9 p_m_c_b  >> p_2bc_2 55:bca d2h^9 p_c_m_a  >> p_2ac_2ac 56 d2h^10 p_c_c_n  >> p_2ab_2ac 56:cab d2h^10 p_n_a_a  >> p_2ac_2bc 56:bca d2h^10 p_b_n_b  >> p_2bc_2ab 57 d2h^11 p_b_c_m  >> p_2c_2b 57:bac d2h^11 p_c_a_m  >> p_2c_2ac 57:cab d2h^11 p_m_c_a  >> p_2ac_2a 57:cba d2h^11 p_m_a_b  >> p_2b_2a 57:bca d2h^11 p_b_m_a  >> p_2a_2ab 57:acb d2h^11 p_c_m_b  >> p_2bc_2c 58 d2h^12 p_n_n_m  >> p_2_2n 58:cab d2h^12 p_m_n_n  >> p_2n_2 58:bca d2h^12 p_n_m_n  >> p_2n_2n 59:1 d2h^13 p_m_m_n:1 >> p_2_2ab_1ab 59:2 d2h^13 p_m_m_n:2  >> p_2ab_2a 59:1cab d2h^13 p_n_m_m:1 >> p_2bc_2_1bc 59:2cab d2h^13 p_n_m_m:2  >> p_2c_2bc 59:1bca d2h^13 p_m_n_m:1 >> p_2ac_2ac_1ac 59:2bca d2h^13 p_m_n_m:2  >> p_2c_2a 60 d2h^14 p_b_c_n  >> p_2n_2ab 60:bac d2h^14 p_c_a_n  >> p_2n_2c 60:cab d2h^14 p_n_c_a  >> p_2a_2n 60:cba d2h^14 p_n_a_b  >> p_2bc_2n 60:bca d2h^14 p_b_n_a  >> p_2ac_2b 60:acb d2h^14 p_c_n_b  >> p_2b_2ac 61 d2h^15 p_b_c_a  >> p_2ac_2ab 61:bac d2h^15 p_c_a_b  >> p_2bc_2ac 62 d2h^16 p_n_m_a  >> p_2ac_2n 62:bac d2h^16 p_m_n_b  >> p_2bc_2a 62:cab d2h^16 p_b_n_m  >> p_2c_2ab 62:cba d2h^16 p_c_m_n  >> p_2n_2ac 62:bca d2h^16 p_m_c_n  >> p_2n_2a 62:acb d2h^16 p_n_a_m  >> p_2c_2n 63 d2h^17 c_m_c_m  >> c_2c_2 63:bac d2h^17 c_c_m_m  >> c_2c_2c 63:cab d2h^17 a_m_m_a  >> a_2a_2a 63:cba d2h^17 a_m_a_m  >> a_2_2a 63:bca d2h^17 b_b_m_m  >> b_2_2b 63:acb d2h^17 b_m_m_b  >> b_2b_2 64 d2h^18 c_m_c_a c_2ac_2 >> # c_2bc_2 64:bac d2h^18 c_c_m_b c_2ac_2ac # >> c_2bc_2bc 64:cab d2h^18 a_b_m_a a_2ab_2ab #  >> a_2ac_2ac 64:cba d2h^18 a_c_a_m a_2_2ab #  >> a_2_2ac 64:bca d2h^18 b_b_c_m b_2_2ab #  >> b_2_2bc 64:acb d2h^18 b_m_a_b b_2ab_2 # b_2bc_2 >> 65 d2h^19 c_m_m_m c_2_2 65:cab >> d2h^19 a_m_m_m a_2_2 65:bca d2h^19 >> b_m_m_m b_2_2 66 d2h^20 c_c_c_m  >> c_2_2c 66:cab d2h^20 a_m_a_a  >> a_2a_2 66:bca d2h^20 b_b_m_b  >> b_2b_2b 67 d2h^21 c_m_m_a c_2a_2 >> # c_2b_2 67:bac d2h^21 c_m_m_b c_2a_2a #  >> c_2b_2b 67:cab d2h^21 a_b_m_m a_2b_2b #  >> a_2c_2c 67:cba d2h^21 a_c_m_m a_2_2b #  >> a_2_2c < Jun2000 >> 67:bca d2h^21 b_m_c_m b_2_2a # b_2_2c >> 67:acb d2h^21 b_m_a_m b_2a_2 # b_2c_2 >> 68:1 d2h^22 c_c_c_a:1 c_2_2_1ac # >> c_2_2_1bc 68:2 d2h^22 c_c_c_a:2 c_2a_2ac >> # c_2b_2bc 68:1bac d2h^22 c_c_c_b:1 c_2_2_1ac >> # c_2_2_1bc 68:2bac d2h^22 c_c_c_b:2 c_2a_2c >> # c_2b_2c 68:1cab d2h^22 a_b_a_a:1 a_2_2_1ab # >> a_2_2_1ac 68:2cab d2h^22 a_b_a_a:2 a_2a_2b #  >> a_2a_2c < Jun2000 >> 68:1cba d2h^22 a_c_a_a:1 a_2_2_1ab # a_2_2_1ac >> 68:2cba d2h^22 a_c_a_a:2 a_2ab_2b # a_2ac_2c >> 68:1bca d2h^22 b_b_c_b:1 b_2_2_1ab # b_2_2_1bc >> 68:2bca d2h^22 b_b_c_b:2 b_2ab_2b # b_2bc_2b >> 68:1acb d2h^22 b_b_a_b:1 b_2_2_1ab # b_2_2_1bc >> 68:2acb d2h^22 b_b_a_b:2 b_2b_2ab # b_2b_2bc >> 69 d2h^23 f_m_m_m f_2_2 70:1 >> d2h^24 f_d_d_d:1 f_2_2_1d 70:2 d2h^24 >> f_d_d_d:2 f_2uv_2vw 71 d2h^25 i_m_m_m  >> i_2_2 72 d2h^26 i_b_a_m  >> i_2_2c 72:cab d2h^26 i_m_c_b  >> i_2a_2 72:bca d2h^26 i_c_m_a  >> i_2b_2b 73 d2h^27 i_b_c_a  >> i_2b_2c 73:bac d2h^27 i_c_a_b  >> i_2a_2b 74 d2h^28 i_m_m_a  >> i_2b_2 74:bac d2h^28 i_m_m_b  >> i_2a_2a 74:cab d2h^28 i_b_m_m  >> i_2c_2c 74:cba d2h^28 i_c_m_m  >> i_2_2b 74:bca d2h^28 i_m_c_m  >> i_2_2a 74:acb d2h^28 i_m_a_m  >> i_2c_2 75 c4^1 p_4 >> p_4 76 c4^2 p_41 >> p_4w 76 c4^2 p_41 p_41 >> 77 c4^3 p_42 p_4c 77 >> c4^3 p_42 p_42 78 c4^4 p_43 >> p_4cw 78 c4^4 p_43 p_43 >> 79 c4^5 i_4 i_4 80 >> c4^6 i_41 i_4bw 81 s4^1 >> p_4 p_4 82 s4^2 i_4 >> i_4 83 c4h^1 p_4/m  >> p_4 84 c4h^2 p_42/m  >> p_4c 84 c4h^2 p_42/m p_42 >> 85:1 c4h^3 p_4/n:1 p_4ab_1ab 85:2 >> c4h^3 p_4/n:2 p_4a 86:1 c4h^4 p_42/n: >> 1 p_4n_1n 86:2 c4h^4 p_42/n:2  >> p_4bc 87 c4h^5 i_4/m  >> i_4 88:1 c4h^6 i_41/a:1 >> i_4bw_1bw 88:2 c4h^6 i_41/a:2  >> i_4ad 89 d4^1 p_4_2_2 >> p_4_2 90 d4^2 p_4_21_2 >> p_4ab_2ab 91 d4^3 p_41_2_2 >> p_4w_2c 91 d4^3 p_41_2_2 p_41_2c >> 92 d4^4 p_41_21_2 p_4abw_2nw 93 >> d4^5 p_42_2_2 p_4c_2 93 d4^5 >> p_42_2_2 p_42_2 94 d4^6 p_42_21_2 >> p_4n_2n 95 d4^7 p_43_2_2 >> p_4cw_2c 95 d4^7 p_43_2_2 p_43_2c >> 96 d4^8 p_43_21_2 p_4nw_2abw 97 >> d4^9 i_4_2_2 i_4_2 98 d4^10 >> i_41_2_2 i_4bw_2bw 99 c4v^1 p_4_m_m >> p_4_2 100 c4v^2 p_4_b_m >> p_4_2ab 101 c4v^3 p_42_c_m >> p_4c_2c 101 c4v^3 p_42_c_m p_42_2c >> 102 c4v^4 p_42_n_m p_4n_2n 103 >> c4v^5 p_4_c_c p_4_2c 104 c4v^6 >> p_4_n_c p_4_2n 105 c4v^7 p_42_m_c >> p_4c_2 105 c4v^7 p_42_m_c >> p_42_2 106 c4v^8 p_42_b_c >> p_4c_2ab 106 c4v^8 p_42_b_c p_42_2ab >> 107 c4v^9 i_4_m_m i_4_2 108 >> c4v^10 i_4_c_m i_4_2c 109 c4v^11 >> i_41_m_d i_4bw_2 110 c4v^12 i_41_c_d >> i_4bw_2c 111 d2d^1 p_4_2_m >> p_4_2 112 d2d^2 p_4_2_c >> p_4_2c 113 d2d^3 p_4_21_m >> p_4_2ab 114 d2d^4 p_4_21_c >> p_4_2n 115 d2d^5 p_4_m_2 >> p_4_2 116 d2d^6 p_4_c_2 >> p_4_2c 117 d2d^7 p_4_b_2 >> p_4_2ab 118 d2d^8 p_4_n_2 >> p_4_2n 119 d2d^9 i_4_m_2 >> i_4_2 120 d2d^10 i_4_c_2 >> i_4_2c 121 d2d^11 i_4_2_m >> i_4_2 122 d2d^12 i_4_2_d >> i_4_2bw 123 d4h^1 p_4/m_m_m  >> p_4_2 124 d4h^2 p_4/m_c_c  >> p_4_2c 125:1 d4h^3 p_4/n_b_m:1 >> p_4_2_1ab 125:2 d4h^3 p_4/n_b_m:2  >> p_4a_2b 126:1 d4h^4 p_4/n_n_c:1 >> p_4_2_1n 126:2 d4h^4 p_4/n_n_c:2  >> p_4a_2bc 127 d4h^5 p_4/m_b_m  >> p_4_2ab 128 d4h^6 p_4/m_n_c  >> p_4_2n 129:1 d4h^7 p_4/n_m_m:1 >> p_4ab_2ab_1ab 129:2 d4h^7 p_4/n_m_m:2  >> p_4a_2a 130:1 d4h^8 p_4/n_c_c:1 >> p_4ab_2n_1ab 130:2 d4h^8 p_4/n_c_c:2  >> p_4a_2ac 131 d4h^9 p_42/m_m_c  >> p_4c_2 132 d4h^10 p_42/m_c_m  >> p_4c_2c 133:1 d4h^11 p_42/n_b_c:1 >> p_4n_2c_1n 133:2 d4h^11 p_42/n_b_c:2  >> p_4ac_2b 134:1 d4h^12 p_42/n_n_m:1 >> p_4n_2_1n 134:2 d4h^12 p_42/n_n_m:2  >> p_4ac_2bc 135 d4h^13 p_42/m_b_c  >> p_4c_2ab 135 d4h^13 p_42/m_b_c p_42_2ab >> 136 d4h^14 p_42/m_n_m p_4n_2n 137:1 >> d4h^15 p_42/n_m_c:1 p_4n_2n_1n 137:2 d4h^15 p_42/ >> n_m_c:2 p_4ac_2a 138:1 d4h^16 p_42/n_c_m:1 >> p_4n_2ab_1n 138:2 d4h^16 p_42/n_c_m:2  >> p_4ac_2ac 139 d4h^17 i_4/m_m_m  >> i_4_2 140 d4h^18 i_4/m_c_m  >> i_4_2c 141:1 d4h^19 i_41/a_m_d:1 >> i_4bw_2bw_1bw 141:2 d4h^19 i_41/a_m_d:2  >> i_4bd_2 142:1 d4h^20 i_41/a_c_d:1 >> i_4bw_2aw_1bw 142:2 d4h^20 i_41/a_c_d:2  >> i_4bd_2c 143 c3^1 p_3 >> p_3 144 c3^2 p_31 >> p_31 145 c3^3 p_32 >> p_32 146:h c3^4 r_3:h >> r_3 146:r c3^4 r_3:r >> p_3* 147 c3i^1 p_3  >> p_3 148:h c3i^2 r_3:h  >> r_3 148:r c3i^2 r_3:r  >> p_3* 149 d3^1 p_3_1_2 >> p_3_2 150 d3^2 p_3_2_1 >> p_3_2" 151 d3^3 p_31_1_2 p_31_2_(0_0_4) >> # p_31_2c_(0_0_1) >> 152 d3^4 p_31_2_1 p_31_2" 153 >> d3^5 p_32_1_2 p_32_2_(0_0_2) # p_32_2c_(0_0_1) >> 154 d3^6 p_32_2_1 p_32_2" 155:h >> d3^7 r_3_2:h r_3_2" 155:r d3^7 >> r_3_2:r p_3*_2 156 c3v^1 p_3_m_1 >> p_3_2" 157 c3v^2 p_3_1_m >> p_3_2 158 c3v^3 p_3_c_1 >> p_3_2"c 159 c3v^4 p_3_1_c >> p_3_2c 160:h c3v^5 r_3_m:h >> r_3_2" 160:r c3v^5 r_3_m:r >> p_3*_2 161:h c3v^6 r_3_c:h >> r_3_2"c 161:r c3v^6 r_3_c:r >> p_3*_2n 162 d3d^1 p_3_1_m  >> p_3_2 163 d3d^2 p_3_1_c  >> p_3_2c 164 d3d^3 p_3_m_1  >> p_3_2" 165 d3d^4 p_3_c_1  >> p_3_2"c 166:h d3d^5 r_3_m:h  >> r_3_2" 166:r d3d^5 r_3_m:r  >> p_3*_2 167:h d3d^6 r_3_c:h  >> r_3_2"c 167:r d3d^6 r_3_c:r  >> p_3*_2n 168 c6^1 p_6 >> p_6 169 c6^2 p_61 >> p_61 170 c6^3 p_65 >> p_65 171 c6^4 p_62 >> p_62 172 c6^5 p_64 >> p_64 173 c6^6 p_63 >> p_6c 173 c6^6 p_63 p_63 >> 174 c3h^1 p_6 p_6 175 >> c6h^1 p_6/m p_6 176 c6h^2 p_63/ >> m p_6c 176 c6h^2 p_63/m  >> p_63 177 d6^1 p_6_2_2 p_6_2 >> 178 d6^2 p_61_2_2 p_61_2_(0_0_5) # p_61_2_(0_0_1) >> 179 d6^3 p_65_2_2 p_65_2_(0_0_1) 180 >> d6^4 p_62_2_2 p_62_2_(0_0_4) # p_62_2c_(0_0_1) >> 181 d6^5 p_64_2_2 p_64_2_(0_0_2) # p_64_2c_(0_0_1) >> 182 d6^6 p_63_2_2 p_6c_2c 182 >> d6^6 p_63_2_2 p_63_2c 183 c6v^1 >> p_6_m_m p_6_2 184 c6v^2 p_6_c_c >> p_6_2c 185 c6v^3 p_63_c_m >> p_6c_2 185 c6v^3 p_63_c_m p_63_2 >> 186 c6v^4 p_63_m_c p_6c_2c 186 >> c6v^4 p_63_m_c p_63_2c 187 d3h^1 p_6_m_2 >> p_6_2 188 d3h^2 p_6_c_2 >> p_6c_2 189 d3h^3 p_6_2_m >> p_6_2 190 d3h^4 p_6_2_c >> p_6c_2c 191 d6h^1 p_6/m_m_m  >> p_6_2 192 d6h^2 p_6/m_c_c  >> p_6_2c 193 d6h^3 p_63/m_c_m  >> p_6c_2 193 d6h^3 p_63/m_c_m p_63_2 >> 194 d6h^4 p_63/m_m_c p_6c_2c 194 >> d6h^4 p_63/m_m_c p_63_2c 195 t^1 >> p_2_3 p_2_2_3 196 t^2 f_2_3 >> f_2_2_3 197 t^3 i_2_3 >> i_2_2_3 198 t^4 p_21_3 >> p_2ac_2ab_3 199 t^5 i_21_3 >> i_2b_2c_3 200 th^1 p_m_3  >> p_2_2_3 201:1 th^2 p_n_3:1 >> p_2_2_3_1n 201:2 th^2 p_n_3:2  >> p_2ab_2bc_3 202 th^3 f_m_3  >> f_2_2_3 203:1 th^4 f_d_3:1 >> f_2_2_3_1d 203:2 th^4 f_d_3:2  >> f_2uv_2vw_3 204 th^5 i_m_3  >> i_2_2_3 205 th^6 p_a_3  >> p_2ac_2ab_3 206 th^7 i_a_3  >> i_2b_2c_3 207 o^1 p_4_3_2 >> p_4_2_3 208 o^2 p_42_3_2 >> p_4n_2_3 209 o^3 f_4_3_2 >> f_4_2_3 210 o^4 f_41_3_2 >> f_4d_2_3 211 o^5 i_4_3_2 >> i_4_2_3 212 o^6 p_43_3_2 >> p_4acd_2ab_3 213 o^7 p_41_3_2 >> p_4bd_2ab_3 214 o^8 i_41_3_2 >> i_4bd_2c_3 215 td^1 p_4_3_m >> p_4_2_3 216 td^2 f_4_3_m >> f_4_2_3 217 td^3 i_4_3_m >> i_4_2_3 218 td^4 p_4_3_n >> p_4n_2_3 219 td^5 f_4_3_c f_4a_2_3 >> # f_4c_2_3 220 td^6 i_4_3_d >> i_4bd_2c_3 221 oh^1 p_m_3_m  >> p_4_2_3 222:1 oh^2 p_n_3_n:1 >> p_4_2_3_1n 222:2 oh^2 p_n_3_n:2  >> p_4a_2bc_3 223 oh^3 p_m_3_n  >> p_4n_2_3 224:1 oh^4 p_n_3_m:1 >> p_4n_2_3_1n 224:2 oh^4 p_n_3_m:2  >> p_4bc_2bc_3 225 oh^5 f_m_3_m  >> f_4_2_3 226 oh^6 f_m_3_c f_4a_2_3 >> # f_4c_2_3 227:1 oh^7 f_d_3_m:1 >> f_4d_2_3_1d 227:2 oh^7 f_d_3_m:2  >> f_4vw_2vw_3 228:1 oh^8 f_d_3_c:1 f_4d_2_3_1ad >> # f_4d_2_3_1cd 228:2 oh^8 f_d_3_c:2 f_4ud_2vw_3 >> # f_4cvw_2vw_3 229 oh^9 i_m_3_m  >> i_4_2_3 230 oh^10 i_a_3_d i_4bd_2c_3 >> >>  >>  >> >> >> >> On 04/09/2006, at 6:01 PM, Bob Hanson wrote: >> >> >>> Dear Dr. Hall, >>> >>> My name is Bob Hanson; I'm a professor at St. Olaf College in >>> Northfield, Minnesota, and also the lead developer of the Jmol >>> molecular visualization application/applet <http:// >>> http://www.stolaf.edu/ academics/chemapps/jmol>. The Jmol applet has >>> rich functionality, one of which is the ability to be read CIF >>> and RES files and to apply the appropriate symmetry operators >>> indicated in these files. A demo of this capability is at >>> <http://fusion.stolaf.edu/chemistry/ jmol/xtalx>. >>> >>> Last week, during a visit to Cambridge I had the opportunity to >>> speak with Peter and Judith MurrayRust, and they suggested we >>> implement a Hall symbol reader into Jmol. >>> >>> I have now done that and wonder if you could answer some >>> questions I have about Hall naming. Do you have the time to work >>> with me a bit on this? If so, here are a few questions for >>> starters, all in relation to <http://cci.lbl.gov/sginfo/ >>> hall_symbols.html>: >>> >>> 1. Default axes. The statement reads: >>> >>> 2. the second rotation (if N is 2) has an axis direction of >>>  a if preceded by an N of 2 or 4 >>>  *a+b* if preceded by an N of 3 or 6 >>> >>> Should this read "ab" rather than "a+b" in that second case? It >>> seems to me that what is intended is that the space group <P 3 >>> 2> is explicity <P 3z 2'> not <P 3z 2">, and 2' is ab, not a+b. >>> >>> 2. In the discussion of Table 4: based on the included list of >>> space groups, which I presume to be complete, it would appear >>> that it is not possible to have 2' or 2" when the preceding axis >>> is NOT Nz. I wonder why there is the discussion there of Nx and >>> Ny in relation to 2' and 2". Is that necessary? >>> 3. I guess my main question relates to the general >>> implementation of Hall symbols. Is it intended that there be >>> exactly one Hall symbol for each possible space group >>> possibility? That is, are there exactly 530 legitimate Hall >>> symbols? Or is it conceivable/ appropriate for people to invent >>> their own equivalent set of Hall symbols for any given space group? >>> >>> Thanks for your time. I look forward to hearing from you. >>> >>> Bob Hanson >>> Professor of Chemistry >>> St. Olaf College >>> http://www.stolaf.edu/people/hansonr >>> >>> >> >> > > 