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. 148

## Table 2.1.2.5

Th. Hahna and M. I. Aroyoc
 Table 2.1.2.5| top | pdf | Graphical symbols of symmetry axes normal to the plane of projection and symmetry points in the plane of the figure
DescriptionAlphanumeric symbolGraphical symbolScrew vector of the defining operation of the screw axis (in units of the shortest lattice translation vector parallel to the axis)Symmetry elements represented by the graphical symbol
2 None 2
Twofold screw axis: 2 sub 1' 21
3 None 3
Threefold screw axis: 3 sub 1' 31
Threefold screw axis: 3 sub 2' 32
4 None 4
Fourfold screw axis: 4 sub 1' 41
Fourfold screw axis: 4 sub 2' 42
Fourfold screw axis: 4 sub 3' 43
6 None 6
Sixfold screw axis: 6 sub 1' 61
Sixfold screw axis: 6 sub 2' 62
Sixfold screw axis: 6 sub 3' 63
Sixfold screw axis: 6 sub 4' 64
Sixfold screw axis: 6 sub 5' 65
None
Inversion axis: 3 bar' None
Inversion axis: 4 bar' None
Inversion axis: 6 bar' None
Twofold rotation axis with centre of symmetry None
Twofold screw axis with centre of symmetry
Fourfold rotation axis with centre of symmetry None
4 sub 2' screw axis with centre of symmetry
Sixfold rotation axis with centre of symmetry None
6 sub 3' screw axis with centre of symmetry

Notes on the heights' h of symmetry points , , and :

(1) Centres of symmetry and , as well as inversion points and on and axes parallel to [001], occur in pairs at heights' h and . In the space-group diagrams, only one fraction h is given, e.g. stands for and . No fraction means and . In cubic space groups, however, because of their complexity, both fractions are given for vertical axes, including and .

(2) Symmetries and contain vertical and axes; their and inversion points coincide with the centres of symmetry. This is not indicated in the space-group diagrams.

(3) Symmetries and also contain vertical and axes, but their and inversion points alternate with the centres of symmetry; i.e. points at h and interleave with or points at and . In the tetragonal and hexagonal space-group diagrams, only one fraction for and one for or is given. In the cubic diagrams, all four fractions are listed for ; e.g. (223): : ; : .