Written Definition:
 

                                   A rotation fixes one point in the plane and turns the rest of it some angle
                                   around that point. In general a rotation could be by any angle, but for patterns
                                   like we have, the angle has to divide 360°, and a little more analysis finds further
                                   restrictions. In fact, the angle of rotation can only be 180°, 120°, 90°, or 60°.
                                   The order of a rotation is the number of times it has to be performed to bring the
                                   plane back to where it started. So a 60°-rotation has order 6, a 90°-rotation has
                                   order 4, a 120°-rotation has order 3, and an 180°-rotation has order 2. A 180°
                                   rotation is also called a half turn.

Diagrammed: