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. 149

Table 2.1.2.6 

Th. Hahna and M. I. Aroyoc

Table 2.1.2.6| top | pdf |
Graphical symbols of symmetry axes parallel to the plane of projection

DescriptionGraphical 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
Twofold rotation axis [Scheme scheme62] None 2
Twofold screw axis: `2 sub 1' [Scheme scheme63] [{1 \over 2}] [2_{1}]
Fourfold rotation axis [Scheme scheme64] [Scheme scheme70] None 4
Fourfold screw axis: `4 sub 1' [Scheme scheme65] [{1 \over 4}] [4_{1} ]
Fourfold screw axis: `4 sub 2' [Scheme scheme66] [{1 \over 2}] [4_{2} ]
Fourfold screw axis: `4 sub 3' [Scheme scheme67] [{3 \over 4}] [4_{3} ]
Inversion axis: `4 bar' [Scheme scheme68] None [\bar{4}, 2]
Inversion point on `4 bar' axis [Scheme scheme69] None None
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.