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The intersection of four balls of radius s centered at the vertices of a regular tetrahedron with side length s is called the Reuleaux tetrahedron, but its surface is not a surface of constant width.[70] It can, however, be made into a surface of constant width, called Meissner's tetrahedron, by replacing three of its edge arcs by curved surfaces, the surfaces of rotation of a circular arc. 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.[
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