Quinquadecagon

A quinquadecagon is a polygon with fifteen sides and fifteen vertices. In a regular quinquadecagon, all sides are equal in length and all interior angles are equal. The sum of the interior angles of any quinquadecagon is (15-2) * 180 degrees, which equals 13 * 180 degrees or 2340 degrees. For a regular quinquadecagon, each interior angle measures 2340 / 15 degrees, which is 156 degrees.

The construction of a regular quinquadecagon is possible using only a compass and straightedge. This was demonstrated by Carl Friedrich Gauss, who proved that a regular n-gon can be constructed if n is a product of a power of 2 and distinct Fermat primes. Fifteen is the product of 3 and 5, both of which are Fermat primes (F0=3 and F1=5), thus a regular quinquadecagon is constructible. The central angle subtended by each side of a regular quinquadecagon at its center is 360 / 15 degrees, which equals 24 degrees.