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Symmetry dictionary (symCIF) version 1.0.1

_space_group_symop.generator_xyz

Name:
'_space_group_symop.generator_xyz'

Definition:

   A parsable string giving one of the symmetry generators of the
   space group in algebraic form.  If W is a matrix representation
   of the rotational part of the generator defined by the positions
   and signs of x, y and z, and w is a column of translations
   defined by the fractions, an equivalent position X' is
   generated from a given position X by

             X' = WX + w.

   (Note: X is used to represent the bold italic x in International
   Tables for Crystallography Volume A, Section 5.)

   When a list of symmetry generators is given, it is assumed
   that the complete list of symmetry operations of the space
   group (including the identity operation) can be generated
   through repeated multiplication of the generators, that is,
   (W3, w3) is an operation of the space group if (W2,w2) and
   (W1,w1) [where (W1,w1) is applied first] are either operations
   or generators and:

           W3 = W2 x W1
           w3 = W2 x w1 + w2.

   Ref: International Tables for Crystallography (2002). Volume A,
        Space-group symmetry, edited by Th. Hahn, 5th ed.
        Dordrecht: Kluwer Academic Publishers.

Example:

x,1/2-y,1/2+z c glide reflection through the plane (x,1/4,z) chosen as one of the generators of the space group

Type: char

Mandatory item: no

Related item: _space_group_symop.operation_xyz (alternate)

Enumeration default: x,y,z

Category: space_group_symop