Rubiks Revenge

A 4x4x4 variation of RubiksCube. What I like about this is the internal mechanism: inside the cube is a sphere with grooves dividing the sphere into eight sections. The small pieces of the cube are designed to slide along these grooves. There are no springs or special moving parts. This is quite neat because it combines two of the most basic shapes, a sphere and a cube, in a novel way to create wonderfully elegant design.

But my 4x4x4 cube is not so elegant in its implementation: the eight pieces of the sphere that surround the grooves are held on by little screws. Sometimes one of the small cubes catches the edge of one of the face plates, twisting it out of shape. So now when I turn a face of the cube, it often gets stuck on one of these twisted faces and the little cube pops out. This is frustrating, yet when a single piece pops out the whole cube crumbles in my hands --- surely only a very elegant design would fall apart completely due to one popped-out piece!

Putting the 4x4x4 cube back together is an interesting task, since you get to see various overlapping cylinders that are the key to its design. typ

The thing is, though, that this cube is only slightly more difficult to solve than the ordinary 3x3x3 one. For example, to adapt the algorithm I use for Rubik's to RR, I simply: 1) solve the inner 2z2x2 cube, as if its cube-faces were the corner pieces of a 3x3x3 cube; 2) using some easily-discovered sequences to change edge-piece pairings without messing up the inner cube, get each edge piece paired with its identical twin; 3) now that the cube has been reduced to a 3x3x3, solve it as such, ignoring the center creases altogether. There's one slight hitch: On a 3x3x3 cube, the center of each face is fixed; they cannot move relative to each other. On the 4x4x4 it is possible to do this, so you have to study the corner cubies to determine the proper relationship of the centers, before you can do step 1) above.