Fourfold Screw Axes (4n)

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The symbols above show fourfold screw axes perpendicular to the plane of the screen, i.e parallel to Z. A fourfold screw axis is equivalent to an anticlockwise rotation of 90° about a line followed by a translation parallel to that line. The translation is either 1/4, 1/2, or 3/4 of the repeat distance in the lattice along the axis for four-one, four-two, and four-three screw axes, respectively. A four-one screw axis with a fourfold rotation about the c-axis, i.e. about the line 0,0,z, followed by a translation of 1/4 c along it, will have the corresponding symmetry operator -y,x,1/4+z.

Note that four-one and four-three are equivalent except for handedness (right- and left-handed, respectively), in contrast to the four-two axis which has no handedness. These axes have the written symbols "41", "42", and "43", respectively.

In space group diagrams for cubic symmetry, fourfold screw axes are shown along both X and Y directions as well as along the Z direction when present. A fractional value next to the symbol indicates the height of the axis of rotation above the XY plane.

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