Quiz

A polyhedron can lie on its face if its center of gravity is projected onto that face. (Here, the center of gravity must be projected orthogonally onto the plane in which the face lies. :) ) Since it turns out that the polyhedron must be convex, otherwise it will not be possible for it to lie on any of its faces, the center of gravity is located inside the polyhedron, which means that if perpendiculars are dropped from it onto all the faces, then at least one of them must intersect the face onto which it is dropped.