International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

International Tables for Crystallography (2006). Vol. A, ch. 1.4, p. 7

Section 1.4.2. Symmetry planes parallel to the plane of projection

Th. Hahna*

aInstitut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany
Correspondence e-mail: hahn@xtal.rwth-aachen.de

1.4.2. Symmetry planes parallel to the plane of projection

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Symmetry planeGraphical symbolGlide vector in units of lattice translation vectors parallel to the projection planePrinted symbol
Reflection plane, mirror plane [Scheme scheme14] None m
`Axial' glide plane [Scheme scheme15] [{1 \over 2}] lattice vector in the direction of the arrow a, b or c
`Double' glide plane (in centred cells only) [Scheme scheme16] [\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 scheme17] [\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; in centred cells only) [Scheme scheme18] [{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 2.2.6[link] ).
For further explanations of the `double' glide plane e see Note (iv)[link] below and Note (x)[link] in Section 1.3.2[link] .
§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.








































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