enneakaidecagon

An enneakaidecagon is a polygon with nineteen sides and nineteen vertices. The word "enneakaidecagon" is derived from the Greek words "enneakaideka" meaning seventeen and "gonia" meaning angle. Thus, it is also sometimes referred to as a heptadecagon or a 17-gon.

In a regular enneakaidecagon, all sides are of equal length, and all interior angles are equal. The sum of the interior angles of any enneakaidecagon, whether regular or irregular, is given by the formula (n-2) * 180 degrees, where n is the number of sides. For an enneakaidecagon, this sum is (19-2) * 180 = 17 * 180 = 3060 degrees.

The measure of each interior angle in a regular enneakaidecagon is 3060 / 19 degrees, which is approximately 161.05 degrees. The measure of each exterior angle in a regular enneakaidecagon is 360 / 19 degrees, which is approximately 18.95 degrees.

While the construction of a regular enneakaidecagon using only a compass and straightedge is possible, it is a complex geometric feat. This is related to the fact that 19 is a prime number but not a Fermat prime.

The enneakaidecagon is not a commonly encountered polygon in everyday life or in many areas of mathematics compared to figures with fewer sides. However, it exists as a valid geometric shape with specific properties.