The symmetry of crystals. Symmetry elements
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The symmetry elements in crystals are geometric operations by means of which we relate an atom (ion, or molecule), located in the unit cell, with other ones that are equivalent (symetrically equivalent). To represent the symmetry elements in crystallography we use graphical and numerical symbols as shown in the following table… Below you will also find several examples of symmetry elements applied to the repetition of objects, in this case represented by a hand, or a circle...

Numeric and graphical symbols for the symmetry elements

Símbolos gráficos y numéricos que representan a los elementos de simetría. Imagen tomada de las Tablas Internacionales de Cristalografía.
More information about the meaning of these symbols can be seen through this link to the University College London

Making use of some animated representations made available at the Bucknell University, we represent here (with no animation) some of the most common operations of the symmetry elements, using hands and circles:

2-fold axis2-fold axis

Two-fold axis    2

3-fold axis3-fold axis

Three-fold axis    3

4-fold axis4-fold axis
Four-fold axis    4

6-fold axis6-fold axis

Six-fold axis   6

2-fold screw axis2-fold screw axis
Two-fold screw axis    21

mirror planemirror plane
Mirror plane    m

glide planeglide plane
Glide plane   a, b, c

inversion centerinversion center

Inversion center   1

4-fold improper axis of rotation
The two blue-colored hands (left hands) are on a lower plane than the white ones (right hands).

Four-fold improper axis of rotation   4

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