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Question

Order of rotational symmetry of a octagon is _____


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Solution

Step 1: Define rotational symmetry and then find the order of rotational symmetry of an octagon.

  • Rotation turns an object about a fixed point. This fixed point is the center of rotation.
  • The angle by which the object rotates is the angle of rotation. A half-turn means rotation by 180°; a quarter-turn means rotation by 90°. Rotation may be clockwise or anticlockwise.
  • If, after a rotation, an object looks exactly the same, we say that it has rotational symmetry.
  • In a complete turn (of 360° ), the number of times an object looks exactly the same is called the order of rotational symmetry. The order of symmetry of a square, for example, is 4 while, for an equilateral triangle, it is 3.

Step 2: Find the order of rotational symmetry of an octagon.

An octagon will look exactly the same after every 45° rotation when it rotates 360°. Therefore the number of times the figure coincides with its original position is 8.

Hence the Order of rotational symmetry of an octagon is 8.


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