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)).
Read more about this topic: Reuleaux Triangle
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