Symmetry planes inclined to the plane of projection (in cubic space groups of classes  and  only)

Hahn, Th.

doi:10.1107/97809553602060000503

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

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International Tables for Crystallography (2006). Vol. A. ch. 1.4, p. 8

Section 1.4.3. Symmetry planes inclined to the plane of projection (in cubic space groups of classes $[\overline{4}{3m}]$ and $[m\overline{3}m]$ only)

Th. Hahn^a ^*

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

1.4.3. Symmetry planes inclined to the plane of projection (in cubic space groups of classes $[\overline{4}{3m}]$ and $[m\overline{3}m]$ only)

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Symmetry plane	Graphical symbol^† for planes normal to		Glide vector in units of lattice translation vectors for planes normal to		Printed symbol
Symmetry plane	[011] and $[[01\bar{1}]]$	[101] and $[[10\bar{1}]]$	[011] and $[[01\bar{1}]]$	[101] and $[[10\bar{1}]]$	Printed symbol
Reflection plane, mirror plane			None	None	m
`Axial' glide plane			$[{1 \over 2}]$ lattice vector along [100]	$[\left.\!\matrix{{1 \over 2}\hbox{ lattice vector along }[010]\hfill\cr\noalign{\vskip 29pt}\cr{1 \over 2}\hbox{ lattice vector along }[10\bar{1}]\cr\hbox{ or along }[101]\hfill\cr}\right\}]$	a or b
`Axial' glide plane			$[{1 \over 2}]$ lattice vector along $[[01\bar{1}]]$ or along [011]		a or b
`Double' glide plane^‡ [in space groups $[I\bar{4}3m]$ (217) and $[Im\bar{3}m]$ (229) only]			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			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; in centred cells only)			$[{1 \over 2}]$ along $[[1\bar{1}1]]$ or along [111]^¶	$[\left.\matrix{{1 \over 2}\hbox{ along }[\bar{1}11]\hbox { or}\cr \hbox{along }[111]\cr\noalign{\vskip 30pt} {1 \over 2}\hbox{ along }[\bar{1}\bar{1}1]\hbox{ or}\cr \hbox{ along }[1\bar{1}1]}\right\}]$ ^¶	d
			$[{1 \over 2}]$ along $[[\bar{1}\bar{1}1]]$ or along $[[\bar{1}11]]$ ^¶		d

^† 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'.
^‡For further explanations of the `double' glide plane e see Note (iv)

below and Note (x)

in Section 1.3.2

.
^§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.
^¶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).
^††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.

References

International Tables for Crystallography (2006). Vol. A. ch. 1.4, p. 8

Section 1.4.3. Symmetry planes inclined to the plane of projection (in cubic space groups of classes and only)

1.4.3. Symmetry planes inclined to the plane of projection (in cubic space groups of classes and only)

References

Section 1.4.3. Symmetry planes inclined to the plane of projection (in cubic space groups of classes $[\overline{4}{3m}]$ and $[m\overline{3}m]$ only)

1.4.3. Symmetry planes inclined to the plane of projection (in cubic space groups of classes $[\overline{4}{3m}]$ and $[m\overline{3}m]$ only)