Someone asked what is the maximum size tetrahedron is hidden in a sphere! Going down this rabbit hole has been more fun than a barrel of monkeys. Geometricians have determined that the four peaks of such a tetrahedron (TH) lie on four points on the surface of the sphere exactly 0.81D from each other, where D is the diameter of the sphere. So 0.81D is the length of the six edges of the TH. The whole TH can be turned on a lathe because the four faces of the TH are perpendicular to a turning axis containing a peak and the center of the sphere. Sure enough this TH started inside a sphere. The big advantage of turning it instead of sawing it is that one can turn profiles on the four faces, concave, convex etc. I chose convex shapes I rather like. This TH is not finished yet but I would love to know what turners are doing or have done over the decades with turning THs, as well as any other polygons. Can anybody refer me to such??
