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", "62", "63", "64", and "65", respectively.

© Copyright 1995-2006.  Birkbeck College, University of London. Author(s): Jeremy Karl Cockcroft