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
Octagon of 24 faces in a Petrie polygon projection plane of the tesseract. The list defines the number of solutions as 8, by the 8 orientations of this one dissection. These squares and rhombs are used in the Ammann–Beenker tilings. A skew octagon is a skew polygon with 8 vertices and edges but not existing on the same plane. The interior of such an octagon is not generally defined. A "skew zig-zag octagon" has vertices alternating between two parallel planes. A regular skew octagon is vertex-transitive with equal edge lengths. In 3-dimensions it will be a zig-zag skew octagon and can