Reuleaux tetrahedron

thingiverse

The Reuleaux tetrahedron is formed by four spheres of radius s centered at the vertices of a regular tetrahedron with side length s. The spherical surface of each sphere passes through the other three vertices, which also become vertices of the Reuleaux tetrahedron. As a result, the center of each sphere lies on the surfaces of the other three spheres. The Reuleaux tetrahedron has the same face arrangement as a regular tetrahedron but with curved faces: four vertices and four curved faces connected by six circular-arc edges. Printing several of these shapes and placing a piece of wood on top reveals an interesting phenomenon: no matter how you move the wood, it remains the same distance from the floor or table.