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 1.4.1. Symmetry planes normal to the plane of projection (three dimensions) and symmetry lines in the plane of the figure (two dimensions)

Th. Hahna*

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

1.4.1. Symmetry planes normal to the plane of projection (three dimensions) and symmetry lines in the plane of the figure (two dimensions)

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Symmetry plane or symmetry lineGraphical symbolGlide vector in units of lattice translation vectors parallel and normal to the projection planePrinted symbol
[\left.\openup3pt\matrix{\hbox{Reflection plane, mirror plane}\hfill\cr \hbox{Reflection line, mirror line (two dimensions)}\cr}\right\}] [Scheme scheme8] None m
[\left.\openup3pt\matrix{\hbox{`Axial' glide plane}\hfill\cr\hbox{Glide line (two dimensions)}\cr}\right\}] [Scheme scheme9] [\!\openup2pt\matrix{{1 \over 2} \hbox{lattice vector along line in projection plane}\cr {1 \over 2} \hbox{lattice vector along line in figure plane}\hfill\cr}] [\!\matrix{a,\ b \hbox{ or } c\cr g\hfill\cr}]
`Axial' glide plane [Scheme scheme10] [{1 \over 2}] lattice vector normal to projection plane a, b or c
`Double' glide plane (in centred cells only) [Scheme scheme11] [\!\openup2pt\matrix{Two\hbox{ glide vectors:}\hfill\cr{1 \over 2}\hbox{ along line parallel to projection plane and}\cr{1 \over 2} \hbox{ normal to projection plane}\hfill}] e
`Diagonal' glide plane [Scheme scheme12] [\openup2pt\matrix{One\hbox{ glide vector with }two\hbox{ components:}\hfill\cr{1 \over 2}\hbox{ along line parallel to projection plane,}\hfill\cr{1 \over 2}\hbox{ normal to projection plane}\hfill}] n
`Diamond' glide plane (pair of planes; in centred cells only) [Scheme scheme13] [{1 \over 4}] along line parallel to projection plane, combined with [{1 \over 4}] normal to projection plane (arrow indicates direction parallel to the projection plane for which the normal component is positive) d
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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