Reuleaux Triangle - Three-dimensional Version

Three-dimensional Version

The intersection of four spheres of radius s centered at the vertices of a regular tetrahedron with side length s is called the Reuleaux tetrahedron, but is not a surface of constant width. It can, however, be made into a surface of constant width, called Meissner's tetrahedron, by replacing its edge arcs by curved surface patches. Alternatively, the surface of revolution of a Reuleaux triangle through one of its symmetry axes forms a surface of constant width, with minimum volume among all known surfaces of revolution of given constant width (Campi, Colesanti & Gronchi (1996)).