rotational symmetry

crystallography

Written by

The Information Architects of Encyclopaedia Britannica

Last updated

July 13, 2026

Quick Summary

In crystallography, rotational symmetry is a fundamental property describing how atoms are arranged in crystalline solids. This property means that if a crystal is rotated around an imaginary axis, its atomic arrangement will appear unchanged after a specific angle of rotation.12

The possible rotational symmetries in crystals are limited to rotations of 360° divided by n, where n can be 1, 2, 3, 4, or 6. These rotations, along with other symmetry elements like translation, reflection, and inversion, determine the crystal's overall shape and influence its physical characteristics. For instance, a sixfold rotation means the crystal repeats its appearance six times during a full 360° turn, occurring every 60°.12

Summary created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

2 Britannica Sources

Ask Britannica AI about this topic

Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.

symmetry
…such element of symmetry is rotation; other elements are translation, reflection, and inversion. The elements of symmetry present in a particular crystalline solid determine its shape and affect its physical properties.
Read More
…such element of symmetry is rotation; other elements are translation, reflection, and inversion. The elements of symmetry present in a particular crystalline solid determine its shape and affect its physical properties.
Read More

liquid crystal
Symmetries of solids and liquids
Rotational symmetries can be considered in a similar fashion. From one point in empty space, the view is the same regardless of which direction one looks. There is continuous rotational symmetry—namely, the symmetry of a perfect sphere. In the crystal shown in Figure 1A, however,…
Read More
Rotational symmetries can be considered in a similar fashion. From one point in empty space, the view is the same regardless of which direction one looks. There is continuous rotational symmetry—namely, the symmetry of a perfect sphere. In the crystal shown in Figure 1A, however,…
Read More

quasicrystal
Microscopic images of quasicrystalline structures
…pentagons, with axes of fivefold rotational symmetry passing through them. That is to say, rotations about this axis by 72° leave the appearance of the grain unchanged. In a full 360° rotation the grain will repeat itself in appearance five times, once every 72°. There are also axes of twofold…
Read More
…pentagons, with axes of fivefold rotational symmetry passing through them. That is to say, rotations about this axis by 72° leave the appearance of the grain unchanged. In a full 360° rotation the grain will repeat itself in appearance five times, once every 72°. There are also axes of twofold…
Read More