Solids Circumscribing Spheres.

The article demonstrates that the two consequences of tetrahedrons circumscribing a sphere also holds true for more general solids called circumsolids whose faces can be both planar and curved. Any plane through the center of the inscribed sphere divides the circumsolid into two smaller solids whose surface areas are equal if and only if they have equal volumes. The centroid of the boundary surface of a circumsolid and the centroid of its volume are also collinear always with the center of the inscribed sphere at distances in the ratio of four is to three from the center.