heptacontagon

A heptacontagon is a polygon with 70 sides and 70 vertices. The term is derived from the Greek words "heptakont" meaning seventy and "gonia" meaning corner or angle. Like any polygon, a heptacontagon can be convex or concave, and it can be regular or irregular.

In a regular heptacontagon, all sides are of equal length, and all interior angles are equal. The sum of the interior angles of any heptacontagon, regardless of regularity, is given by the formula (n-2) * 180 degrees, where n is the number of sides. For a heptacontagon, this sum is (70-2) * 180 = 68 * 180 = 12240 degrees.

For a regular heptacontagon, each interior angle measures 12240 / 70 degrees, which simplifies to approximately 174.86 degrees. The exterior angle of a regular heptacontagon is 360 / 70 degrees, approximately 5.14 degrees.

A heptacontagon can be constructed using a compass and straightedge if and only if it is a regular heptacontagon and the number of sides (70) can be factored into a product of distinct Fermat primes and a power of 2. The prime factorization of 70 is 2 * 5 * 7. Since 7 is not a Fermat prime, a regular heptacontagon cannot be constructed using only a compass and straightedge.

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