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).
Helix angle In helical and worm gears, the helix angle denotes the standard pitch circle unless otherwise specified.[1] Application of the helix angle typically employs a magnitude ranging from 15° to 30° for helical gears, with 45° capping the safe operation limit. The angle itself may be cut with either a right-hand or left-hand orientation.[5] In its typical parallel arrangement, meshing helical gears requires that the helix angles are of the same magnitude and cut oppositely .