Data Item _space_group.transform_Pp_abc


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Item Description

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
 a-1/4, b-1/4, c-1/4
 b-1/2, c-1/2, a-1/2

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[][ \t_(),.;:"&<>/\{}'`~!@#$%?+=*A-Za-z0-9|^-]*