of the regular octagon. Each subgroup symmetry allows one or more degrees of freedom for irregular forms. Only the g8 subgroup has no degrees of freedom but can seen as directed edges. Use The octagonal shape is used as a design element in architecture. The Dome of the Rock has a characteristic octagonal plan. The Tower of the Winds in Athens is another example of an octagonal structure. The octagonal plan has also been in church architecture such as St. George's Cathedral, Addis Ababa, Basilica of San Vitale (in Ravenna, Italia), Castel del Monte (Apulia, Italia), Florence Baptistery, Zum Friedefürsten Church (Germany) and a number of octagonal churches in Norway. The central space in the Aachen Cathedral, the Carolingian Palatine Chapel, has a regular octagonal floorplan. Uses of octagons in churches also include lesser design elements, such as the octagonal apse of Nidaros Cathedral. Architects such as John Andrews have used octagonal floor layouts in buildings for functionally separating office areas from building services, such as in the Intelsat Headquarters of Washington or Callam Offices in Canberra. Derived figures Related polytopes The octagon, as a truncated square, is first in a sequence of truncated hypercubes: As an expanded square, it is also first in a sequence of expanded hypercubes: See also Bumper pool Hansen's small octagon Octagon house Octagonal number Octagram Octahedron, 3D shape with eight faces. Oktogon, a major intersection in Budapest, Hungary Rub el Hizb (also known as Al Quds Star and as Octa Star) Smoothed octagon References External links Octagon Calculator Definition and properties of an octagon With interactive animation 8 (number) Constructible polygons Polygons by the number of sides Elementary shapes