Rubik's Evil Uncle's Cube - a simply complex problem.

[PaulHDear]

You are provided with a simple, unmarked cube. Three steel rods pass through the cube (crossing at its centre), through the opposing faces (the three rods are the three orthogonal axes of the cube).

 

You are allowed to turn the cube around any of the three rods, subject to the following rules:

1) All rotations must be exactly 45° (in either direction, that is positive or negative).

2) You cannot rotate around the same rod twice in succession.

 

The cube is initially square-on to you, and you must start by making one 45° rotation around the rod of your choice.

 

Your challenge? To restore the cube exactly to its original orientation, or to prove that it cannot be done in a finite number of moves.

 

(NOTE: rule (2) means that you cannot reverse your sequence of rotations, since this would mean a positive and then a negative rotation about the same rod).