sestrigintagon

A sestrigintagon is a polygon with 63 sides and 63 vertices. The term itself is derived from Latin and Greek roots, with "sesta" meaning six, "triginta" meaning thirty, and "gonia" meaning angle. Therefore, sestrigintagon literally translates to "sixty-three-angled."

In Euclidean geometry, a regular sestrigintagon has all sides of equal length and all interior angles equal. The measure of each interior angle of a regular sestrigintagon can be calculated using the formula (n-2) * 180 / n, where n is the number of sides. For a sestrigintagon, this means each interior angle measures (63-2) * 180 / 63 = 61 * 180 / 63, which simplifies to approximately 174.29 degrees.

The sum of the interior angles of any sestrigintagon, regular or irregular, is given by the formula (n-2) * 180 degrees. For a sestrigintagon, this sum is (63-2) * 180 = 61 * 180 = 10980 degrees.

While theoretically possible, constructing a regular sestrigintagon with high precision using only a compass and straightedge is not possible, as 63 is not a product of a power of 2 and distinct Fermat primes. Sestrigintagons are rarely encountered in practical applications due to their complexity and the difficulty of their construction and representation.