Solid Directional Rubix Cube (super-super-cube)

For a normal Rubix cube, we only solve for colors, when the colors of each face are the same, the directions/orientations may not be consistent if they are distinguishable (see the left and middle cube in the image below).

Moreover, for a normal cube, we only solve the outermost layer. However, when the outermost layer is solved, the inner layers may not be solved if they are present (see the middle and right cube in the image below).

Thus, in terms of the total number of configurations given the same size, a solid-directional Rubix cube (super-super-cube, the right cube) is more complex than a directional Rubix cube (super-cube, the middle cube), which in turn is more complex than a standard Rubix cube (the left cube), as shown in the diagram below:

You can download my solid-directional Rubix Cube (super-super-cube) Simulator for free at sscube.zip

The program can record all your moves and allow you to goto any earlier or later step. You can also save or load a cube with all the history in shuffling and solving. For a NxNxN Rubix cube, shuffling will take N^3 steps.

Just take a look at the 15x15x15 super-super-cube as shown in the left image above. At a first glance, it seems incredibly and extraordinarily complicated to solve. The main problem is that you cannot see inner cubies clearly. My program allows you to highlight a specific layer as shown in the right image above. You can also download my sample solution at a.rubix, the solution starts at the 3376th (=15^3+1) step, although it is incomplete (I do not have that much time), but it is sufficient to illustrate the general approach.