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

International Tables for Crystallography (2016). Vol. A, ch. 2.1, p. 147

Table 2.1.2.4 

Th. Hahna and M. I. Aroyoc

Table 2.1.2.4| top | pdf |
Graphical symbols of symmetry planes inclined to the plane of projection (in cubic space groups of classes [\overline{4}{3m}] and [m\overline{3}m] only)

DescriptionGraphical symbol for planes normal toGlide vector(s) (in units of the shortest lattice translation vectors) of the defining operation(s) of the glide plane normal toSymmetry element represented by the graphical symbol
[011] and [[01\bar{1}]][101] and [[10\bar{1}]][011] and [[01\bar{1}]][101] and [[10\bar{1}]]
Reflection plane, mirror plane [Scheme scheme25] [Scheme scheme31] None None m
`Axial' glide plane [Scheme scheme26] [Scheme scheme32] [{1 \over 2}] along [100] [\left.\!\matrix{{1 \over 2}\hbox{ along }[010]\hfill\cr\noalign{\vskip 38pt}\cr{1 \over 2}\hbox{ along }[10\bar{1}]\cr\hbox{ or along }[101]\hfill\cr}\right\}] a or b
`Axial' glide plane [Scheme scheme27] [Scheme scheme33] [{1 \over 2}] along [[01\bar{1}]] or along [011]
`Double' glide plane [in space groups [I\bar{4}3m] (217) and [Im\bar{3}m] (229) only] [Scheme scheme28] [Scheme scheme34] Two glide vectors: [{1 \over 2}] along [100] and [{1 \over 2}] along [[01\bar{1}]] or [{1 \over 2}] along [011] Two glide vectors: [{1 \over 2}] along [010] and [{1 \over 2}] along [[10\bar{1}]] or [{1 \over 2}] along [101] e
`Diagonal' glide plane [Scheme scheme29] [Scheme scheme35] One glide vector: [{1 \over 2}] along [[11\bar{1}]] or along [111] One glide vector: [{1 \over 2}] along [[11\bar{1}]] or along [111] n
`Diamond' glide plane§ (pair of planes) [Scheme scheme30] [Scheme scheme36] [{1 \over 2}] along [[1\bar{1}1]] or along [111] [\left.\matrix{{1 \over 2}\hbox{ along }[\bar{1}11]\hbox { or}\cr \hbox{along }[111]\cr\noalign{\vskip 40pt} {1 \over 2}\hbox{ along }[\bar{1}\bar{1}1]\hbox{ or}\cr \hbox{ along }[1\bar{1}1]}\right\}] d
[{1 \over 2}] along [[\bar{1}\bar{1}1]] or along [[\bar{1}11]]
The symbols represent orthographic projections. In the cubic space-group diagrams, complete orthographic projections of the symmetry elements around high-symmetry points, such as [0,0,0]; [{1 \over 2},0,0]; [{1 \over 4},{1 \over 4},0], are given as `inserts'.
In the space groups [F\bar{4}3m] (216), [Fm\bar{3}m] (225) and [Fd\bar{3}m] (227), the shortest lattice translation vectors in the glide directions are [{\bf t}(1, {1 \over 2}, \bar{{1 \over 2}}\,)] or [{\bf t}(1, {1 \over 2}, {1 \over 2}\,)] and [{\bf t}(\,{1 \over 2}, 1, \bar{{1 \over 2}}\,)] or [{\bf t}(\,{1 \over 2}, 1, {1 \over 2}\,)], respectively.
§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.
The glide vector is half of a centring vector, i.e. one quarter of the diagonal of the conventional body-centred cell in space groups [I\bar{4}3d] (220) and [Ia\bar{3}d] (230).