>...The 1 is definitely no place holder. It has a very significant meaning.
Not sure why place holders are inimical to significance. I think you are saying that the 1 tells you there is no rotation here, like the 0 in the number 201 tells you there are no tens in that number. I call that a place holder. To check myself I looked up its definition, and serendipitously found its mathematical definition "a significant zero in the decimal representation of a number." 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
