Question

Order of rotational symmetry of a octagon is _____

Answer 1

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 $8$.