When 3 cubes interpentrate in an optimal way they create dozens of smaller closed bounded volumes ... like M. C. Escher's Waterfall picture with the cube-3 compound. For Escher's 3 interpenetrating cube figure, what is the count of all the interior and exterior closed bounded volumes? Are there any references to an answer to this?
http://mathworld.wolfram.com/Cube3-Compound.html
Ron