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

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. Hahna*

aInstitut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany
Correspondence e-mail:

1.4.6. Symmetry axes parallel to the plane of projection

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Symmetry axisGraphical symbolScrew vector of a right-handed screw rotation in units of the shortest lattice translation vector parallel to the axisPrinted symbol (partial elements in parentheses)
Twofold rotation axis [Scheme scheme56] None 2
Twofold screw axis: `2 sub 1' [Scheme scheme57] [{1 \over 2}] [2_{1}]
Fourfold rotation axis [Scheme scheme58] [Scheme scheme64] None 4 (2)
Fourfold screw axis: `4 sub 1' [Scheme scheme59] [{1 \over 4}] [4_{1} ] [(2_{1})]
Fourfold screw axis: `4 sub 2' [Scheme scheme60] [{1 \over 2}] [4_{2} ] [(2)]
Fourfold screw axis: `4 sub 3' [Scheme scheme61] [{3 \over 4}] [4_{3} ] [(2_{1})]
Inversion axis: `4 bar' [Scheme scheme62] None [\bar{4} ] [(2)]
Inversion point on `4 bar'-axis [Scheme scheme63] [\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.

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