Intuitive Notion of Rotational  Symmetry
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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.

 

                       
                Order 4                                Order 2                              Order 3                              Order 1
                                                                                                                                         no rotational symmetry

Signs may possess rotational symmetry.


 

                                                                           
            Order 2                             Order 4                                 Order 8                              Order 1 
                                                                                                                                                                           no rotational symmetry

Designs and patterns may possess rotational symmetry.


 

          
         Order 12                      Order 5                       Order 7                      Order 7                       Order 5

Hubcaps may possess rotational symmetry (disregarding center logo).

 

 
        H      I      N      O      S      X      Z

Letters may possess rotational symmetry.
 (The order may vary depending upon the style of the letter.  For example, the letter O
could have order 2 if the O is elongated or order infinite if the O is circular.)

 

 

                 
    

Grid patterns may possess rotational symmetry.

 These each have a rotational symmetry of order 4.

 

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 0º and 360º.  The angles of 0º and 360º are excluded since nothing new happens.

A regular hexagon has
rotational symmetry of
60º, 120º, 180º, 240º, and 300º.

 

The order is order 6.