There are various types of Symmetry; here, three Symmetry are described: (i) Plane of Symmetry, (ii) Axis of Symmetry and (iii) centre of Symmetry
When an imaginary plane can divide a crystal into two parts such that one is the exact mirror image of the other, the crystal is said to have a plane of Symmetry.
Axis of Symmetry
An axis of Symmetry is a line about which the crystal may be rotated to present the same or similar appearance more than once during the complex revolution.
For example, in the case of a cube, an axis passing perpendicularly through the centre is such that when the cube is rotated, it presents a similar appearance in three rotations of 90˚ each and the same appearance after the fourth rotation. Such an axis is called a four-fold axis (figure a). The same or similar appearance is repeated after an angle of 180˚; the axis is called a two-fold or a dial axis (fig b). If the same appearance is repeated after an angle of 120˚, the axis is called a three-fold or triad axis (fig c). the same appearance is repeated after an angle of 60˚ in the case of a hexagonal crystal; the axis is called a six-fold or hexad axis (fig d).
Various axes of symmetry
If the same appearance of a crystal is repeated on rotation through an angle of 360˚/n around an imaginary axis, the axis is called an n-fold axis.
A crystal has only 2-fold, 3-fold, 4-fold and 6-fold axes of rotation.
Centre of Symmetry
The Centre of Symmetry of a crystal is such a point that any line drawn through it intersects the surface of the crystal at an equal distance in both directions.
Crystal has any number of planes or axes of Symmetry but only one center of Symmetry.
