Sexdecagons

A sexdecagon is a polygon with sixteen sides and sixteen vertices. In a regular sexdecagon, all sides are of equal length and all interior angles are equal. The sum of the interior angles of any sexdecagon, regular or irregular, is 2520 degrees. The measure of each interior angle in a regular sexdecagon is 157.5 degrees.

The area of a regular sexdecagon with side length 'a' can be calculated using the formula Area = 4a² cot(π/16). The area can also be expressed in terms of its apothem 'r' as Area = 16 * (1/2) * a * r, which simplifies to Area = 8ar. The apothem itself can be calculated as r = (a/2) cot(π/16).

A regular sexdecagon can be constructed using a straightedge and compass, as 16 is a product of powers of two (16 = 2⁴). This means that it is a constructible polygon. Historically, sexdecagons have appeared in various forms of art and architecture, often as decorative elements or in geometric patterns.