What is rotational symmetry?

Rotation means turning of an object about a fixed point. The fixed point is known as the centre of rotation. The angle of turning during the rotation is called the angle of rotation. If an object looks exactly the same after rotation, it is said to have  rotational symmetry. In a complete rotation, the number of times an object looks exactly the same is known as the order of rotational symmetry.

 

For example: Consider the rotation of the following floral design.

 

Here, the angle of rotation is 90° and in a full turn, there are precisely four positions when the figure looks exactly the same. Therefore, it has a rotational symmetry of order four.