Lynnclaire, You mentioned the possibility of 2 144 Polyhedra coming together to form a V.P. This is possible.
The 144 Poly model I made shows that you can take a cube and on each of the 6 faces, you can add a "cap". So, there is a cube in every 144.
The distance from the center of a square face to the top of a cap is the same distance from the cube's center of volume to a cube's face center.
This means that is you take 2 of the 144's, each with a cube in them, and bring them together so that 2 cube faces touch, then you have the 2 144's interpenetrating each other. The interpenetration is exactly the same as for 2 spheres interpenetrating to define the V.P. That is, each sphere surface passes throught the center of volume of the other sphere.
Here are some images: