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
David Van Gelder Octagon House David Van Gelder Octagon House The David Van Gelder Octagon House, also known as Springside is located at 21 Walnut Street in Catskill, New York. The brick house was built in 1860. It is architecturally significant as an example of an octagon house. The eight-sided plan was made popular in the mid-19th century by phrenologist Orson Squire Fowler. He called the floor plan "a superior plan". It includes four large square rooms and four small triangular rooms on each of the two floors. Two corners of each of the triangular rooms are small triangular closets. A central stair rises through