18gons

An 18-gon, also known as an octadecagon, is a polygon with eighteen sides and eighteen vertices. In a regular 18-gon, all sides are of equal length and all interior angles are equal. The measure of each interior angle in a regular 18-gon can be calculated using the formula (n-2) * 180 / n, where n is the number of sides. For an 18-gon, this is (18-2) * 180 / 18 = 16 * 180 / 18 = 16 * 10 = 160 degrees. The sum of the interior angles of any 18-gon, regular or irregular, is (18-2) * 180 = 16 * 180 = 2880 degrees.

The exterior angles of a regular 18-gon each measure 360 / 18 = 20 degrees. The number of diagonals in an 18-gon can be found using the formula n(n-3)/2, which for n=18 is 18(18-3)/2 = 18*15/2 = 9*15 = 135 diagonals.

In geometry, the construction of a regular 18-gon using only a compass and straightedge is not possible. This is because the number of sides, 18, has prime factors that include 3, which is not a Fermat prime. However, it can be constructed with the aid of a marked ruler (neusis construction) or other tools.