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

Hahn, Th.

doi:10.1107/97809553602060000503

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

pdf | chapter contents | chapter index | related articles

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. Hahn^a ^*

^a Institut 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)

| top | pdf |

Symmetry plane or symmetry line	Glide vector in units of lattice translation vectors parallel and normal to the projection plane	Printed symbol
$[\left.\openup3pt\matrix{\hbox{Reflection plane, mirror plane}\hfill\cr \hbox{Reflection line, mirror line (two dimensions)}\cr}\right\}]$	None	m
$[\left.\openup3pt\matrix{\hbox{`Axial' glide plane}\hfill\cr\hbox{Glide line (two dimensions)}\cr}\right\}]$	$[\!\openup2pt\matrix{{1 \over 2} \hbox{lattice vector along line in projection plane}\cr {1 \over 2} \hbox{lattice vector along line in figure plane}\hfill\cr}]$	$[\!\matrix{a,\ b \hbox{ or } c\cr g\hfill\cr}]$
`Axial' glide plane	$[{1 \over 2}]$ lattice vector normal to projection plane	a , b or c
`Double' glide plane^† (in centred cells only)	$[\!\openup2pt\matrix{Two\hbox{ glide vectors:}\hfill\cr{1 \over 2}\hbox{ along line parallel to projection plane and}\cr{1 \over 2} \hbox{ normal to projection plane}\hfill}]$	e
`Diagonal' glide plane	$[\openup2pt\matrix{One\hbox{ glide vector with }two\hbox{ components:}\hfill\cr{1 \over 2}\hbox{ along line parallel to projection plane,}\hfill\cr{1 \over 2}\hbox{ normal to projection plane}\hfill}]$	n
`Diamond' glide plane^‡ (pair of planes; in centred cells only)	$[{1 \over 4}]$ 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)

below and Note (x)

in Section 1.3.2

.
^‡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. 7