Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 2.1, p. 146


Th. Hahna and M. I. Aroyoc

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Graphical symbols of symmetry planes parallel to the plane of projection

DescriptionGraphical symbolGlide vector(s) of the defining operation(s) of the glide plane (in units of the shortest lattice translation vectors parallel to the projection plane)Symmetry element represented by the graphical symbol
Reflection plane, mirror plane [Scheme scheme20] None m
`Axial' glide plane [Scheme scheme21] [{1 \over 2}] in the direction of the arrow a, b or c
`Double' glide plane [Scheme scheme22] [\!\matrix{Two\hbox{ glide vectors:}\hfill\cr{1 \over 2}\hbox{ in either of the directions of the two arrows}}] e
`Diagonal' glide plane [Scheme scheme23] [\!\matrix{One\hbox{ glide vector with }two\hbox{ components}\cr{1 \over 2}\hbox{ in the direction of the arrow}\hfill}] n
`Diamond' glide plane§ (pair of planes) [Scheme scheme24] [{1 \over 2}] in the direction of the arrow; the glide vector is always half of a centring vector, i.e. one quarter of a diagonal of the conventional face-centred cell d
The symbols are given at the upper left corner of the space-group diagrams. A fraction h attached to a symbol indicates two symmetry planes with `heights' h and [h + {1 \over 2}] above the plane of projection; e.g. [{1 \over 8}] stands for [h = {1 \over 8}] and [{5 \over 8}]. No fraction means [h = 0] and [{1 \over 2}] (cf. Section[link]).
The graphical symbols of the `e'-glide planes are applied to the diagrams of seven orthorhombic A-, C- and F-centred space groups, five tetragonal I-centred space groups, and five cubic F- and I-centred space groups.
§Glide planes d occur only in orthorhombic F space groups, in tetragonal I space groups, and in cubic I and F space groups. They always occur in pairs with alternating glide vectors, for instance [{1 \over 4}({\bf a} + {\bf b})] and [{1 \over 4}({\bf a} - {\bf b})]. The second power of a glide reflection d is a centring vector.