Symmetry Elements in a Crystal

Crystals show symmetry because their atoms are arranged in a regular, repeating pattern in three dimensions.

A symmetry operation moves parts of a crystal without changing its overall appearance.

One of the simplest symmetry operations is translation. In translation, every point in the structure moves by the same distance in the same direction, reproducing the repeating lattice.

Other common symmetry operations include rotation, reflection, and inversion. Rotation turns the structure around an axis by a specific angle without changing its appearance. Reflection forms a mirror image across a plane. Inversion moves each point through a central point to an equivalent position on the opposite side.

The geometric feature about which a symmetry operation is performed is called a symmetry element. For instance, a line represents a rotation axis, a plane represents a mirror plane, and a point represents a center of inversion.

Crystals may also contain combined symmetry elements. For example, a screw axis combines rotation with translation along the same axis.

Similarly, a glide plane combines reflection with translation parallel to the plane.