Octagon 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° (formula_1 radians). The central angle is 45° (formula_2 radians). The area of a regular octagon of side length "a" is given by In terms of the circumradius "R", the area is In terms of the apothem "r" (see also inscribed figure), the area is These last two coefficients bracket the value of pi, the area of the unit circle. The area can also be expressed as where
Angle trisection angles can be trisected. For example, for any constructible angle , an angle of measure can be trivially trisected by ignoring the given angle and directly constructing an angle of measure . There are angles that are not constructible but are trisectible (despite the one-third angle itself being non-constructible). For example, is such an angle: five angles of measure combine to make an angle of measure , which is a full circle plus the desired . For a positive integer , an angle of measure is "trisectible" if and only if does not divide . In contrast, is "constructible" if