Recently, I've success to prove that given a Rubik's Cube which has been solved, any sequences of moves will lead it to the original position if repeat long enough. But now I'm wonder that:
Is there any sequences of moves that lead the Rubik's Cube to show up all of its possible permutations before go back to the original position?
According to this Wikipedia article, there are exactly $43,252,003,274,489,856,000$ possible permutations that can be reached solely by turning the sides of the cube. Such a sequences of moves must pass exactly $43,252,003,274,489,856,000$ permutations and go back to the original position right after.