Reuleaux polygon

A Reuleaux triangle replaces the sides of an equilateral triangle by circular arcs

Regular Reuleaux polygons

Irregular Reuleaux heptagon

In geometry, a Reuleaux polygon is a curve of constant width made up of circular arcs of constant radius.^[1] These shapes are named after their prototypical example, the Reuleaux triangle, which in turn is named after 19th-century German engineer Franz Reuleaux.^[2] The Reuleaux triangle can be constructed from an equilateral triangle by connecting each pair of adjacent vertices with a circular arc centered on the opposing vertex, and Reuleaux polygons can be formed by a similar construction from any regular polygon with an odd number of sides as well as certain irregular polygons. Every curve of constant width can be accurately approximated by Reuleaux polygons. They have been applied in coinage shapes.

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