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4. Printed symbols for symmetry operations

A complete set of print symbols was designed by W. Fischer & E. Koch (ITA83, §11.2) and was extensively applied in the Symmetry Operations sections of the space-group descriptions.

In short, each symbol consists of up to three parts. The first part is a single character (sometimes with an index) which describes the kind of operation. The following part(s) give(s) the components of any relevant shift or translation vector - always in parentheses - and the coordinates of the operation's geometric element, in that order.

The Ad-hoc Committee, after considering this system, wishes to introduce two modifications for glide reflections:

(i) instead of the present first character (which may be a, b, c, n, d or g), always write the letter g;

(ii) always write the glide-vector components (in parentheses) in full, in particular for the simple glide reflections in a-, b- or c-glide planes where they were previously omitted.

Rule (i) suppresses information about the kind of glide plane to which the operation belongs. Very often that information is irrelevant or even confusing. For a/b/c planes the suppression can destroy essential information, but the loss is restored by rule (ii) as shown in the example below.

By adopting these changes, the uniformity of symbols - also with respect to those for rotations - is greatly improved. For instance, the symbol of the glide reflection in the plane $x = \frac{1}{4}$, with the unusual glide vector $(0, \frac{1}{2}, -1)$, namely $g(0, \frac{1}{2}, 1) \frac{1}{4}yz$, now falls in line with that for a simple b-glide reflection. In ITA83 the latter was denoted by $b \frac{1}{4} y z$, but this is changed by rule (ii) into $g(0, \frac{1}{2}, 0) \frac{1}{4} y z$.

The above rules apply equally to glide reflections belonging to the element set of a mirror plane. Thus, if the shift component of such an operation is (0, 1, 2), then its symbol begins with g(0, 1, 2), not with m(0, 1,2).

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