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 of parallelism Angle of parallelism In hyperbolic geometry, the angle of parallelism formula_1, is the angle at one vertex of a right hyperbolic triangle that has two asymptotic parallel sides. The angle depends on the segment length "a" between the right angle and the vertex of the angle of parallelism. Given a point off of a line, if we drop a perpendicular to the line from the point, then "a" is the distance along this perpendicular segment, and "φ" or formula_1 is the least angle such that the line drawn through the point at that angle does not intersect the given line.