On Sunday, 20 April 2014 10:14:56 AM Ethan Merritt wrote:
> On Sunday, 20 April 2014 01:35:33 AM Bernhard Rupp wrote:
> > Hi Fellows,
> >
> >
> >
> > because confusion is becoming a popular search term on the bb, let me admit
> > to one more:
> >
> > What is the proper class name for the 65 space groups (you know, those):
> >
> >
> >
> > Are
> >
> > (a) these 65 SGs the chiral SGs and the 22 in the 11 enantiomorphic pairs
> > the enantiomorphic SGs?
> >
> > Or
> >
> > (b) the opposite?
> >
> >
> >
> > In other words, is (a) enantiomorphic a subclass of chiral or (b) chiral a
> > subclass of enantiomorphic?
>
> I am not sure it is possible to reconcile conflicting uses
> of the term "chiral" in formal theory and common use.
>
> My recollection from group theory is that a chiral group is one
> that contains a chiral operator as one of its generators.
> Removing this chiral operator creates 2 smaller groups which are
> not themselves "chiral" because they do not contain the chiral
> operator. Each is a subgroup of the original chiral group.
>
> Translating to crystallography, this would mean that a chiral
> group necessarily contains a mirror or inversion operator.
> Strangely, this is exactly opposite to what I think most
> crystallographers want the term to mean.
>
> I don't recall encountering the term "enantiomorphic group" when
> learning group theory, but as used in crystallography it would
> logically describe one of the two groups, call them SL and SR,
> whose composition SL x SR yields a chiral group containing both
> SL and SR as subgroups.
Sorry - that should be "union" not "composition".
Ethan
