icosinonagons

An icosinonagon is a polygon with 21 sides and 21 vertices. The term is derived from the Greek words "eikosi" meaning twenty and "ennea" meaning nine, combined with "gonia" meaning corner or angle. In geometry, the number of sides of a polygon dictates its classification. Therefore, an icosinonagon is a specific type of 21-gon.

The properties of any polygon can be calculated based on the number of its sides. For a regular icosinonagon, where all sides are of equal length and all interior angles are equal, the sum of the interior angles is given by the formula (n-2) * 180 degrees, where n is the number of sides. For an icosinonagon, this sum is (21-2) * 180 = 19 * 180 = 3420 degrees. Each interior angle of a regular icosinonagon measures 3420 / 21, which is approximately 162.86 degrees.

The exterior angle of a regular icosinonagon is 360 / 21 degrees, approximately 17.14 degrees. The number of diagonals in an icosinonagon can be calculated using the formula n(n-3)/2, which for n=21 results in 21(21-3)/2 = 21 * 18 / 2 = 189 diagonals. While not commonly encountered in everyday geometry, the icosinonagon exists as a mathematical concept within the broader study of polygons.