Intuitive Notion of Rotational Symmetry
An object has rotational symmetry if there is a center point around which the object is turned (rotated) a certain number of degrees and the object looks the same. The number of positions in which the object looks exactly the same is called the order of the symmetry. When determining order, the last rotation returns the object to its original position. Order 1 implies no true rotational symmetry since a full 360 degree rotation was needed.
Definition: A geometric figure has rotational symmetry if the figure is the image of itself under a rotation about a point through any angle whose measure is strictly between 0° and 360°. The angles of 0° and 360° are excluded since nothing new happens.
A regular hexagon has rotational symmetry of 60°, 120°, 180°, 240°, and 300°.
The order is order 6.