Symmetry, in geometry, is a correspondence, or matching, of parts of an object. These parts correspond in size, shape, and position after certain geometric operations are carried out. One major use of the concept of symmetry is to classify crystals (see Crystal ). In this application, three kinds of symmetry are especially useful. The operations that produce these symmetries occur relative to (1) a plane of symmetry, (2) an axis of symmetry, and (3) a center of symmetry.
A plane of symmetry
divides an object into two symmetrical parts. These parts are mirror images of each other—that is, the reflection of one of the parts matches the other part. This kind of symmetry is therefore called reflectional symmetry.
An axis of symmetry
is an imaginary line through the center of an object. Rotating the object about this line produces a number of identical appearances of the object. For example, a square-based pyramid displays four identical appearances when rotated 360° about its axis of symmetry. The number of identical appearances displayed in a 360° rotation is known as the fold of the axis. Thus, the pyramid has a fourfold axis of symmetry.
A center of symmetry
is a midpoint of an object. Located at equal distances from this point are equal and opposite pairs of parts. In crystals, such parts include faces, edges, and corners.
