octodecagonal

An octodecagonal shape is a polygon with 18 sides and 18 angles. The term "octodecagonal" is derived from the Latin words "octo" meaning eight, and "decem" meaning ten, combined with the Greek suffix "-gonia" meaning angle. This results in a polygon that can be thought of as a combination of two octagonal shapes, hence the prefix "octodeca-".

The interior angle of a regular octodecagon can be calculated using the formula for the interior angle of a regular polygon, which is (n-2) * 180/n, where n is the number of sides. For an octodecagon, n = 18, so the interior angle is (18-2) * 180/18 = 160 degrees.

Octodecagonal shapes can be found in various contexts, including architecture, design, and mathematics. In architecture, they can be seen in the design of some buildings and structures. In design, they can be used to create patterns and motifs. In mathematics, they are studied as part of the broader field of polygon geometry.

The area of a regular octodecagon can be calculated using the formula A = (1/4) * n * s^2 * cot(pi/n), where n is the number of sides and s is the length of a side. For an octodecagon, this simplifies to A = (1/4) * 18 * s^2 * cot(pi/18).

The perimeter of a regular octodecagon is simply the sum of the lengths of its sides, which is 18 * s, where s is the length of a side.