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If it rotates 120°, its position looks the same as its initial position.

1 3 2 1

3 2 2 1 1 3 3 2
Initial position 120° 120° + 120° = 240° 240° + 120° = 360°
Here, we can see the ceiling fan gets the same shape as its initial position 3 times at 120°, 240°,
and 360° angles.

Order of Rotational Symmetry

A complete turn or full turn means rotation through 360°. In a complete turn, there are mainly 4
rotational positions.
(i) Rotation through 90°
(ii) Rotation through 180°

(iii) Rotation through 270°
(iv) Rotation through 360°.

The above rotations are called as quarter turn, half turn, three-fourth turn, and full turn
respectively.
The number of times a figure fits onto itself in a complete rotation is called the order of rotational

symmetry. If the angle of rotation of an object is x°, then
360°
Order of rotational symmetry =
° x

Clearly, the ceiling fan has 3 order of rotational symmetry, as if it is rotated through 120°, 240°,
or 360° about the centre point (clockwise or anticlockwise), then it exactly fits with its original
position.

360°
So, order of rotational symmetry of ceiling fan = = 3
120°

Have you ever made a picture that looks symmetrical, but you do not find any line of symmetry.

However, if you rotate it by 180° about the fixed point, the picture will look exactly the same.
Thus, a picture has a rotational symmetry.

Initial position 90° 180° 270° 360°

On rotation through the angles 180° and 360° the given picture looks exactly the same.
Thus, we can say it has a rotational symmetry of order 2.

247 Symmetry