Reinhardt polygon

In geometry, a Reinhardt polygon is an equilateral polygon inscribed in a Reuleaux polygon. As in the regular polygons, each vertex of a Reinhardt polygon participates in at least one defining pair of the diameter of the polygon. Reinhardt polygons with ${\displaystyle n}$ sides exist, often with multiple forms, whenever ${\displaystyle n}$ is not a power of two. Among all polygons with ${\displaystyle n}$ sides, the Reinhardt polygons have the largest possible perimeter for their diameter, the largest possible width for their diameter, and the largest possible width for their perimeter. They are named after Karl Reinhardt, who studied them in 1922.^[1][2]