duosexagintagons

A duosexagintagon is a polygon with 62 sides and 62 vertices. The term "duosexagintagon" is derived from the Latin words "duo" (two), "sexaginta" (sixty), and the Greek word "gonia" (angle). As with any polygon, a duosexagintagon can be either convex or concave, regular or irregular.

In a regular duosexagintagon, all sides are of equal length, and all interior angles are equal. The measure of each interior angle in a regular duosexagintagon can be calculated using the formula (n-2) * 180 / n, where n is the number of sides. For a duosexagintagon, this would be (62-2) * 180 / 62, which simplifies to 60 * 180 / 62, or approximately 174.19 degrees. The sum of the interior angles of any duosexagintagon, regular or irregular, is (62-2) * 180, which equals 10800 degrees.

The exterior angles of a regular duosexagintagon each measure 360 / 62 degrees, or approximately 5.81 degrees. The sum of the exterior angles of any convex duosexagintagon is always 360 degrees.

The construction of a regular duosexagintagon using only a compass and straightedge is not possible, as 62 is not a product of a power of two and distinct Fermat primes. Specifically, the prime factorization of 62 is 2 * 31. Since 31 is a prime number but not a Fermat prime (Fermat primes are of the form 2^(2^n) + 1, such as 3, 5, 17, 257, and 65537), a regular duosexagintagon cannot be constructed with these tools.