hecatontagon

A hecatontagon is a polygon with 100 sides and 100 vertices. The term comes from the Greek words "hekaton" meaning one hundred and "gonia" meaning angle or corner.

Like any regular polygon, a regular hecatontagon has all sides equal in length and all interior angles equal. The measure of each interior angle in a regular hecatontagon can be calculated using the formula (n-2) * 180 / n, where n is the number of sides. For a hecatontagon, this is (100-2) * 180 / 100 = 98 * 180 / 100 = 176.4 degrees. The sum of the exterior angles of any convex polygon is always 360 degrees. For a regular hecatontagon, each exterior angle measures 360 / 100 = 3.6 degrees.

A regular hecatontagon can be constructed using a straightedge and compass, as 100 can be factored into powers of 2 and distinct Fermat primes (100 = 2^2 * 5^2). However, 5 is not a Fermat prime, so this is not directly applicable in the standard Gauss-Wantzel theorem sense which relies on factors being distinct Fermat primes. Nevertheless, construction is possible.

While not commonly encountered in everyday geometry, the concept of a hecatontagon is important in abstract mathematical contexts and in theoretical discussions of polygons with a large number of sides.