Sixfold Screw Axes (61, 62,
63, 64, 65)
The symbols above show sixfold screw axes perpendicular to the
plane of the screen, i.e parallel to Z.
A sixfold screw axis is equivalent to an anticlockwise rotation of 60°
about a line followed by a translation parallel to that line.
The translation is either 1/6, 1/3, 1/2, 2/3, or 5/6 of the repeat distance
in the lattice along the axis for six-one, six-two, six-three, six-four, and
six-five screw axes, respectively. A six-one screw axis with
a sixfold rotation about the c-axis, i.e. about
the line 0,0,z, followed by a translation of 1/6 c
along it, will have
the corresponding symmetry operator x-y,x,1/6+z.
Note that six-one and six-five are equivalent
except for handedness (right- and left-handed, respectively) as
are six-two and six-four screw axes,
in constrast to the six-three axis which has no handedness.
These axes have the written symbols "61",