64gon

A 64-gon is a polygon with 64 sides. It is a type of polygon that falls under the category of many-sided polygons, specifically those with more than 20 sides. The term "gon" is derived from the Greek word "gonia," meaning angle, and the prefix "hexa-" meaning six, but in the case of a 64-gon, the prefix "hecta-" is used to denote 100, and "tetra-" is used to denote four, resulting in "hecta-tetra-gon."

The internal angle of a regular 64-gon can be calculated using the formula for the internal angle of a regular polygon, which is (n-2) * 180 / n, where n is the number of sides. For a 64-gon, this would be (64-2) * 180 / 64 = 177.1875 degrees. The external angle, which is the angle between two adjacent sides, would be 180 - 177.1875 = 2.8125 degrees.

A 64-gon can be constructed using a compass and straightedge, but the process is complex and requires precise measurements. It is also possible to construct a 64-gon using a regular 64-sided star polygon, which is a type of star polygon with 64 vertices.

In geometry, 64-gons are less commonly studied than polygons with fewer sides, such as triangles, quadrilaterals, and pentagons. However, they can be useful in certain mathematical and practical applications, such as in the design of complex shapes and patterns, or in the study of symmetry and tiling.