Did you know that the diagonals of the faces of a cube can be joined to form the framework of a tetrahedron?

I just read about this today. It seems that things should not work out so nicely. It would be nice to see a sculpture of the cube with a tetrahedron inside it.

Choose a face of a cube and draw a diagonal on it. The vertices at each end of the diagonal are shared by two other faces. From each vertex draw the connecting diagonals to the two other faces. That leaves one more face to be connected to the others. The lines form the outline of a tetrahedron.