icosidigon

An icosidigon is a polygon with 20 sides. The term is derived from Greek words meaning "twenty" and "angle". Like any polygon, an icosidigon has 20 vertices and 20 edges. The sum of the interior angles of any icosidigon is given by the formula (n-2) * 180 degrees, where n is the number of sides. For an icosidigon, this means the sum of interior angles is (20-2) * 180 = 18 * 180 = 3240 degrees.

A regular icosidigon has all sides equal in length and all interior angles equal. In a regular icosidigon, each interior angle measures 3240 degrees / 20 = 162 degrees. The exterior angle of a regular icosidigon is 18 degrees. The number of diagonals in an icosidigon can be calculated using the formula n(n-3)/2, which for n=20 results in 20(20-3)/2 = 20*17/2 = 170 diagonals.

Icosidigons can be convex or concave, depending on the arrangement of their vertices. A convex icosidigon has all interior angles less than 180 degrees, while a concave icosidigon has at least one interior angle greater than 180 degrees. The study of icosidigons falls under the broader field of geometry, specifically polygons.