Symmetry     

If we represent a (non-square) rectangle by an envelope, we see that there are just four ways of mapping the rectangle onto itself. These are:

•  the identity map I, which leaves its position unchanged
•  the reflection V in a vertical axis
•  the reflection H in a horizontal axis, and
•  the half-turn rotation R.
These are the symmetries of the rectangle. Now for any given rectangular flag, the symmetries of that flag are just those symmetries above which map the flag (with its pattern) onto itself. Check out the symmetries of the following flags.

               

                                                                                             


The Bahamas flag preserves its symmetry under the identity I and the horizontal reflection H.


The Yugoslav flag preserves its symmetry under the identity I and the vertical reflection V.


The Scottish flag preserves it symmetry under all four of the symmetries of the rectangle.


The French flag preserves its symmetry under the identity I and the horizontal reflection H.