# Difference between revisions of "Symmetry"

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## Revision as of 12:17, 19 November 2006

## Basic

### Axes of symmetry

Axes of symmetry have to do with balance of shape when rotated around these imaginary axes.

Every crystal belongs to a particular crystal system (cubic, tetragonal, hexagonal, trigonal, orthorhombic, monoclinic or triclinic) and the symmetry for each of these systems is defined by ideal shapes.

Following is an illustration of symmetry axes in the orthorhobic system.

When determining the axes of symmetry it is important to rotate (or spin) the crystal around that axis through a 360° rotation and judge how many times the exact image is repeated during the rotation.

As can be seen in the above images there are 3 axes of symmetry in the orthorhombic system and each axis produces the same image twice during a 360° spin around that axis.

When an axis shows the same image twice, we name it a 2-fold axis of symmetry (or better: a "digonal axis of symmetry"). So the orthorhombic system is characterized by 3 2-fold axes of symmetry.

Other crystal systems will have less or more axes of symmetry. A 3-fold axis of symmetry means that the image is repeated 3 times (named a "trigonal axis of symmetry") etc.

### Planes of symmetry

Planes of symmetry can be regarded as mirror planes. They divide a crystal in two and each side of the division is the mirror of the other whilst the total image is not altered by the mirror plane (the symmetry stays in tact).

As with the axes of symmetry the orthorhombic system is used for illustration and there are 3 planes of symmetry in this crystal system.

In all the above images the dividing plane acts as a mirror plane. In other crystal systems there may be fewer or more planes of symmetry.

To illustrate that not all divisions by a plane create a symmetry plane, the illustration on the left shows that the mirror transforms the crystal into a kite form instead of its original prismatic shape.

### Center of symmetry

A center of symmetry is the central point from which crystal faces appear the same on either end of the center.

In this image the center of symmetry is where the green, the blue and the red axis of symmetry meet.

## Sources

- Symmetry made easy (images used with permission)