how many angles of rotation does a octagon have
Octagon A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol {8}. The internal angle at each vertex of a regular octagon is 135° (    3 π 4   {\displaystyle \scriptstyle {\frac {3\pi }{4}}}  radians). The central angle is 45° (    π 4   {\displaystyle \scriptstyle {\frac {\pi }{4}}}  radians).
Regular polygon In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter is fixed, or a regular apeirogon, if the edge length is fixed.