Symmetry axes parallel to the plane of projection

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. 10

Section 1.4.6. Symmetry axes parallel to the plane of projection

Th. Hahn^a ^*

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

1.4.6. Symmetry axes parallel to the plane of projection

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Symmetry axis	Screw vector of a right-handed screw rotation in units of the shortest lattice translation vector parallel to the axis	Printed symbol (partial elements in parentheses)
Twofold rotation axis	None	2
Twofold screw axis: `2 sub 1'	$[{1 \over 2}]$	$[2_{1}]$
Fourfold rotation axis	None	4 (2)
Fourfold screw axis: `4 sub 1'	$[{1 \over 4}]$	$[4_{1} ]$ $[(2_{1})]$
Fourfold screw axis: `4 sub 2'	$[{1 \over 2}]$	$[4_{2} ]$
Fourfold screw axis: `4 sub 3'	$[{3 \over 4}]$	$[4_{3} ]$ $[(2_{1})]$
Inversion axis: `4 bar'	None	$[\bar{4} ]$
Inversion point on `4 bar'-axis	–	$[\bar{4}]$ point

^† The symbols for horizontal symmetry axes are given outside the unit cell of the space-group diagrams. Twofold axes always occur in pairs, at `heights' h and $[h + {1 \over 2}]$ above the plane of projection; here, a fraction h attached to such a symbol indicates two axes with heights h and $[h + {1 \over 2}]$ . No fraction stands for [h = 0]

and $[{1 \over 2}]$ . The rule of pairwise occurrence, however, is not valid for the horizontal fourfold axes in cubic space groups; here, all heights are given, including [h = 0]

and $[{1 \over 2}]$ . This applies also to the horizontal $[\bar{4}]$ axes and the $[\bar{4}]$ inversion points located on these axes.

References

International Tables for Crystallography (2006). Vol. A. ch. 1.4, p. 10