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 equation with real coefficients can be solved geometrically with compass, straightedge, and an angle trisector if and only if it has three real roots. A regular polygon with "n" sides can be constructed with ruler, compass, and angle trisector if and only if formula_63 where "r, s, k" ≥ 0 and where the "p" are distinct primes greater than 3 of the form formula_64 (i.e. Pierpont primes greater than 3). For any nonzero integer , an angle of measure radians can be divided into equal parts with straightedge and compass if and only if is either a power of or