Creating a pattern with rotational symmetry
Move the angle slider a (blue) to make rotated copies of polygon BCDEF.
Click the checkbox, then move the angle slider b (red) to rotate the entire pattern.
Move points B, C, D, E, F to change the shape of the polygon.
Move point A to change the center of rotation.
If the rotated (red) pattern lines up with the original (blue) pattern, then the pattern has rotational symmetry, by the angle b.