Zibo,

All things are possible in the computer. My undertanding is that a 4x4x4 is
being built, but I have not heard that it is yet complete.

The real mind-bender is the continuous Rubik Sphere. Take a sphere, slice it
arbitrarily many times. Now each slice makes a plane of rotation and gives a
degree of freedom. The Rubik Cube is a special case for which there is a
mechanical implementation.

Bill