One Wheel
Legend
Wrong. It's possible to swap two edge pieces on a 4×4×4 without swapping anything else. (Fun fact: this is the case for 4×4×4, but on larger even-order cubes, it's not possible to swap just two edge pieces while leaving all the centres and corners intact. Proof is left as an exercise for the reader.)
Does that include hidden layer pieces, as in my 2x2 example?
