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
The Octagon House was occupied by 10 families, probably one living in each room, tenement-apartment-style. The residents were probably mostly workers in the factories that populated Foggy Bottom. In 1898, the American Institute of Architects (AIA) selected the Octagon to be their new national headquarters. They rented the building for 4 years, and then purchased it outright in 1902. The Octagon would continue to serve as AIA's headquarters until the construction of the current headquarters building in the 1960s. The Octagon opened as a museum in 1970. The museum was restored to its 1817–18 era appearance in the early 1990s—the wall colors and