When a structure rotated by an angle between 0° and 360° coincides with the original structure, it is said to have rotational symmetry. The number of times it coincides as it rotates through is known as order of symmetry. For example- Benzene molecule.
Letters H, S, N and Z on rotation by an angle 180 degrees and O by an angle 90 degree clockwise or counterclockwise look the same as the original letter. Therefore, these 5 letters are said to have rotational symmetry.
There are 8 equal sides and 8 equal angles in a regular octagon. Rotating an octagon around its center, the 1/8th of a full-circle rotation will result adjacent sides to coincide with each other.
We know, a circle has 360° and (1/8)th of 360° = 45°.
Therefore, a minimum of 45° rotation in either counterclockwise or clockwise direction is required to put each of the edges over the position where the adjacent edge was located before.
The symmetry of a molecule consists of symmetry operations that are performed to a molecule. There are a total of 5 types of symmetry operations: identity, reflection, inversion, proper rotation, and improper rotation.