WHAT IS ROTATIONAL SYMMETERY?

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.
 
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Generally speaking, an object with rotational symmetry is an object that looks the same after a certain amount of rotation. An object may have more than one rotational symmetry; for instance, if reflections or turning it over are not counted, the triskelion appearing on the Isle of Man's flag (see opposite) has three rotational symmetries (or "a threefold rotational symmetry"). More examples may be seen below. The degree of rotational symmetry is how many degrees the shape has to be turned to look the same on a different side or vertex. It can not be the same side or vertex.

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