More Symmetry
The combination of rotation and inversion results in an inversion axis.
The symbol is n (read n-bar). This is called Hermann-Mauguin notation.
For n = 1, 1 is an inversion center.
For n = 2, n is not used. This operation would be the same as a mirror, m.
A 3 inversion axis is shown to the right.
Below, compare a
The diamond glide, d, is found only in F (face) or I (body) centered cells.
The diamond glide consists of reflection followed by translation of 1/4 along two cell edges.
Screw Axes are a combination of rotation axes and translations.
The symbols are:
21 31 32 41 42 43
61 62 63 64 65
The symbols are of the form
xy
xy
The rotation is 
degrees.
The translation is 
units along the screw axis.
A two-fold screw axis, 21, refers to a rotation of 
or 180 degrees, combined with a translation of
along the screw axis.
+1/2 indicates translation of +1/2 normal to the plane of the page.
(21is read two sub one)
A three-fold screw axis, 31, refers to a rotation of 
or 120 degrees, combined with a translation of 
along the screw axis.
A second operation of the 31 results in the object translated by
along the screw axis.
A three-fold screw axis, 31, refers to a rotation of or 120 degrees, combined with a translation of 
along the screw axis.
A second operation of the 32 results in the object translated by
along the screw axis.
Notice the result is a set of screws that turn in opposite directions.
