# Interdimensional Cubes

Submitted by cubex on Fri, 09/10/2004 - 08:04.

As a thought experiment consider the case of the familar 4x4x4 cube with a 2x2x2 cube embedded inside it, instead of the usual mechanism. I'll call this the "Interdimensional 4x4x4 cube" for lack of a better name. Now clearly if we turn the slices of the 4x4x4 cube it would have an effect on the internal 2x2x2 cube. Now moving the slice adjacent to the U face and moving the slice adjacent to the R face this would be the equivalent of turning the internal 2x2x2's U face and R face.

My question is: Is it possible to reach all the positions of the internal 2x2x2 without having any constraints on the 4x4x4 cube? How many positions are there?

Clearly it is possible to manipulate the internal 2x2x2 cube without touching the 4x4x4 cubes' corners, but what about the centre pieces and edge pieces of the 4x4x4?

My question is: Is it possible to reach all the positions of the internal 2x2x2 without having any constraints on the 4x4x4 cube? How many positions are there?

Clearly it is possible to manipulate the internal 2x2x2 cube without touching the 4x4x4 cubes' corners, but what about the centre pieces and edge pieces of the 4x4x4?