More Symmetry

Index

Inversion Axes

The Diamond Glide

Screw Axes

Inversion Axes

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 3 and S6.

 

 

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The Diamond Glide

 

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.

 

Below, compare the n-glide (left) with the d-glide (right):

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Screw Axes

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.

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