An octagon has eight-fold rotational symmetry, because rotation of octagon by 45 degrees (one-eighth of a full circle) produces a figure that is superimposible on (or congruent to) the original.
Chat with our AI personalities
Rotational symmetry means it will look the same after being rotated a certain amount. Let's assume that you mean a regular octagon where the sides are all equal in length and the angles are all the same (135 degrees). With such an octagon, if you rotate it one turn to the right (that's 45 degrees), it will look just the same. Rotate another 45° and it is still the same. You can do this 8 times so we say that a regular octagon has an order of rotational symmetry of 8.
It has rotational symmetry to the order of 2
A regular octagon has 8 lines of symmetry.
A regular nonagon with 9 sides has a rotational symmetry of 9.
Rotational symmetry of order 1.