Reuleaux Tetrahedron Spheroform with Tetrahedral Symmetry

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A Reuleaux tetrahedron is a solid in which the intersection of four spheres of the same radius are centered at the vertices of a regular tetrahedron. To turn it into a solid of constant width (spheroform), one must radius the edges of the tetrahedron. A Meissner tetrahedron only includes three rounded edges (all edges contacting the same vertex, OR three edges surrounding the same face) to achieve the definition of a spheroform; however, this eliminates tetrahedral symmetry. The model here is a spheroform with tetrahedral symmetry.