Different Types of Symmetry in Cubic Lattices

**Category : **JEE Main & Advanced

(1) **Centre of symmetry :** An imaginary point within the crystal such that any line drawn through it intersects the surface of the crystal at equal distances in both directions.

(2) **Plane of symmetry :** It is an imaginary plane which passes through the centre of a crystal and divides it into two equal portions such that one part is exactly the mirror image of the other.

A cubical crystal possesses six diagonal plane of symmetry and three rectangular plane of symmetry.

(3) **Axis of symmetry :** It is an imaginary straight line about which, if the crystal is rotated, it will present the same appearance more than once during the complete revolution. In general, if the same appearance of a crystal is repeated on rotating through an angle \[\frac{{{360}^{o}}}{n}\], around an imaginary axis, the axis is called an n-fold axis.

**A cubical crystal possesses in all 13 axis of symmetry**

Axis of four-fold symmetry = 3 (Because of six faces) | Axis of three-fold symmetry = 4 (Because of eight corners) | Axis of two-fold symmetry = 6 (Because of twelve edges) |

(4) **Elements of symmetry :** The total number of planes, axes and centre of symmetry possessed by a crystal are termed as elements of symmetry. A cubic crystal possesses a total of 23 elements of symmetry.

Planes of symmetry\[=(3+6)=9\],

Axes of symmetry\[=(3+4+6)=13\],

Centre of symmetry = 1.

Total number of symmetry elements = 23

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