Elements of Symmetry

Crystal Symmetry refers to the ‘balanced’ pattern of the atom structure. In well developed crystals, this ‘balance’ of structure is evident in their outward shape and if a large number of such crystals are examined, it will be found that different species vary in the symmetric, arrangement of their faces. There are three basic elements of symmetry – centre of symmetry, plane of symmetry and axis of symmetry.

A centre of symmetry exists when every face of the perfect crystal is parallel to a similar face diametrically opposite to it on the other side of the crystal.

A plane of symmetry is an imaginary plane dividing a body into two parts, so that each half is the mirror image of the other. If a crystal was cut in half along such a plane and then the cut surface was to be placed against a metal mirror, the reflection would appear to replace the missing half. The number of possible planes of symmetry in a crystal varies from nine (in a cube) to none at all, according to the species of crystals.

An axis of symmetry is an imaginary line through the crystal about which the crystal can be rotated to represent the same appearance two, three, four or six times in one complete rotation of 360°.

• Axis of two-fold or binary or digonal symmetry: During a complete rotation, a similar face appears twice in the same position.
• Axis of three-fold or trigonal symmetry: During a complete rotation a similar face appears thrice in the same position.
• Axis of four-fold or tetragonal symmetry: During a complete rotation a similar face appears four times in the same position.
• Axis of six-fold or hexagonal symmetry: During a complete rotation a similar face appears six times in the same position.

Although for clarity one set of faces is considered in these examples, all other faces in the figures fall similarly into repeat positions i.e. the whole crystal presents a like appearance two, three, four or six times in the revolution.