identigons

Identigons are a type of geometric shape that are formed by connecting the vertices of a regular polygon to the vertices of another regular polygon of the same order, but with a different orientation. The resulting shape is a star-like polygon with equal sides and angles. The number of sides of an identigon is equal to the number of vertices of the original polygon.

Identigons were first studied by the French mathematician Pierre Wantzel in the 19th century. They are a special case of star polygons, which are polygons that are not simple (i.e., their edges intersect). Identigons are simple polygons, meaning their edges do not intersect.

The properties of identigons depend on the number of sides of the original polygon. For example, a 5-sided identigon (a pentagon) has 5 equal sides and 5 equal angles, each measuring 108 degrees. A 6-sided identigon (a hexagon) has 6 equal sides and 6 equal angles, each measuring 120 degrees.

Identigons have been used in various fields, including art, architecture, and mathematics. In art, they have been used to create intricate patterns and designs. In architecture, they have been used to create decorative elements in buildings. In mathematics, they have been used to study the properties of polygons and to explore the relationships between different types of polygons.