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
Trigonometric constants expressed in real radicals number of sides). This is because the sum of the angles of any "n"-gon is 180° × ("n" – 2) and so the measure of each angle of any regular "n"-gon is 180° × ("n" – 2) ÷ "n". Thus for example the entry "45°: square" means that, with "n" = 4, 180° ÷ "n" = 45°, and the number of degrees in each angle of a square is ("n" – 2) × 45° = 90°. For cube roots of non-real numbers that appear in this table, one has to take the principal value, that is the cube root with