Well let me further muddy the waters by insisting that the 1 IS DEFINITELY a place-holder, telling you that there is no rotation (greater than 1-fold) along the a or b axes, and that the 2 therefore refers to 2-fold rotation along the next axis, the ab diagonal (no the -a,b diagonal which is perpendicular to a and c but is symmetry related to the a,b diagonal). just like in the decimal number 102 the zero tells you that the 0 signifies there is no multiple of 10^2 and the 1 must therefore be 1*10^3.
I guess it comes down to whether you see a 1-fold rotation as being a rotation, in which case this is the order of the rotation about a, or as no rotation at all in which case it is a placeholder bumping the "2" on to the third axis. I guess the original question was why can't the 1's be omitted in the short form, as for p21 (P 1 21 1) or C2 (C 1 2 1). Calling it a placeholder to position the "2" then seems a reasonable description. C1 2 1 is like decimal 001, the leading zero's can be dispensed with without creating ambiguity. eab On 02/18/2015 12:05 PM, Pierre Rizkallah wrote:
At the risk of muddying the waters further, the difference between 312 and 321 is that the 2-fold normal to the 3-fold is along the diagonal of the ab face in 312, while it is along the a (or b, by equivalence) in 321. The 1 is definitely no place holder. It has a very significant meaning. The increasing number of apparently redundant numbers in a space group name is not accidental or incremental. It is simply because in e-mail, people could not (in recent history) write the subscripts. So, P3112 used to be written as P 3(1) 1 2, which meant there is a 3sub1 3-fold screw, with a 2-fold normal to it along the diagonal in the ab plane. The round brackets used to save us from confusion, but their use seems to have dropped out from the lexicon. Who'd be a crystallographer today! Pierre Rizkallah -----Original Message----- From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Keller, Jacob Sent: 18 February 2015 16:42 To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] P3212--1's in Space Group Names? Well, I meant no harm to the poor 1 by calling it a placeholder, but that in the case of P3212, the 1 is simply to tell you that there is no rotation about the second axis but is instead about the third. Saying "okay, nothing here" amounts to being a place-holder to avoid ambiguity in assigning the loci of the rotations. Place-holders are important too, e.g. the 0's in 1000, perhaps. Maybe to be rigorous we should start calling p1 "p111?" (not really...) JPK -----Original Message----- From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Kay Diederichs Sent: Wednesday, February 18, 2015 11:05 AM To: CCP4BB@JISCMAIL.AC.UK Subject: Re: [ccp4bb] P3212--1's in Space Group Names? Hmm, "placeholder" for me does not seem to emphasize enough the role that this number plays in the space group names. My understanding (but I fail to remember where I read this ...) is that the first number is the order of the rotation (i.e. 6,4,3,2 or 1) of the unique unit cell axis (often the one with the highest symmetry), the second number is the rotation order of a secondary axis, and the third number gives the rotation order of a tertiary axis - which is the third axis in the orthorhombic system, but a diagonal at least in the trigonal and tetragonal (and I think cubic) systems. This makes it clear that each (baseline) letter in the spacegroup name has its specific role, and tells you about the order of the rotation axis. On top of that comes the screw axis information which is much easier to read when using subscripts. But obviously the naming scheme was chosen such that even if screw axes are not indicated with subscripts, the resulting names are unambiguous. best, Kay
