[IUCr Home Page] [CIF Home Page]


Symmetry dictionary (symCIF) version 1.0.1




   This item specifies the transformation (P,p) of the basis
   vectors from the setting used in the CIF (a,b,c) to the
   reference setting given in _space_group.reference_setting
   (a',b',c'). The value is given in Jones-Faithful notation
   corresponding to the rotational matrix P combined with the
   origin shift vector p in the expression:

        (a',b',c') = (a,b,c)P + p.

   P is a post-multiplication matrix of a row (a,b,c) of column
   vectors. It is related to the inverse transformation (Q,q) by:

        P = Q^-1^
        p = Pq = -(Q^-1^)q.

   These transformations are applied as follows:

   atomic coordinates  (x',y',z') = Q(x,y,z) + q
   Miller indices      (h',k',l') = (h,k,l)P
   symmetry operations         W' = (Q,q)W(P,p)
   basis vectors       (a',b',c') = (a,b,c)P + p

   This item is given as a character string involving the
   characters a, b and c with commas separating the expressions
   for the a', b' and c' vectors. The numeric values may be
   given as integers, fractions or real numbers. Multiplication
   is implicit, division must be explicit. White space within
   the string is optional.


'-b+c, a+c, -a+b+c' R3:r to R3:h
'a-1/4, b-1/4, c-1/4' Pnnn:1 to Pnnn:2
'b-1/2, c-1/2, a-1/2' Bbab:1 to Ccca:2

Mandatory item: no

Category: space_group