Three interpenetrating spheres yield a maximum of seven pieces, not counting pieces that are further subdivided. What is the maximum number of pieces (i.e., completely bounded volumes) that can be formed when three spheres and two tetrahedrons all interpenetrate?
Two triangles and one rectangle mutually interpenetrate, with the base of each triangle and both bases (i.e., both ends) of the rectangle sealed by precisely fitting flat surfaces.
What is the maximum number of pieces, not further subdivided, that can thus be formed, considering, only the surfaces of these three figures as boundaries and counting only pieces that are not further subdivided?
What is the maximum number of pieces, not further subdivided, that can be formed when a square and a triangle all interpenetrate?