Definition
Order of rotational symmetry
The order of rotational symmetry is how many times a figure matches itself during one complete turn.
Continue from this idea into connected AXIO math.
What it means
Rotate the figure about its centre and count each exact match in one full turn. Count the full-turn match once. A square matches at 90°, 180°, 270°, and 360°, so its order is 4.
Remember it
One full spin; count the click-in-place matches.
Example
A non-square rectangle matches its starting position at 180° and again at 360°. Its order of rotational symmetry is 2.
Watch for
The order is a count, not the angle between matches. A figure with no smaller-turn match has order 1 because it matches after the full turn.
Common mix-up
Do not count the starting position and the 360° position as two separate matches; they are the same orientation.
Exact meaning
The order of rotational symmetry of a figure is the number of orientations in one full 360° turn at which the figure coincides exactly with its starting position.