**
Fourfold Screw Axes (4**_{n})
Return link to the symbol table

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 "4_{1}",
"4_{2}", and
"4_{3}", 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.

© Copyright 1997-1999.
Birkbeck College, University of London.