Incenter centers known to the ancient Greeks, and the only one that does not in general lie on the Euler line. It is the first listed center, X(1), in Clark Kimberling's Encyclopedia of Triangle Centers, and the identity element of the multiplicative group of triangle centers. For polygons with more than three sides, the incenter only exists for tangential polygons—those that have an incircle that is tangent to each side of the polygon. In this case the incenter is the center of this circle and is equally distant from all sides. It is a theorem in Euclidean geometry that the three
Frustum volume of a pyramidal frustum whose bases are "n"-sided regular polygons is where "a" and "a" are the sides of the two bases. For a right circular conical frustum and where "r" and "r" are the base and top radii respectively, and "s" is the slant height of the frustum. The surface area of a right frustum whose bases are similar regular "n"-sided polygons is where "a" and "a" are the sides of the two bases. Frustum In geometry, a frustum (plural: "frusta" or "frustums") is the portion of a solid (normally a cone or pyramid) that lies between one