OK, so clicking a “sticker” on a “face” twists that face into a new position without changing it, but why do some 3×3 slices of other faces spin or fly onto other faces?
That is the scrambling (or unscrambling) effect of twisting a “face” on a 4D magic cube. Notice that a twist on the original magic cube doesn’t change the state of the stickers on that face, but it does affect the state of adjacent faces. Notice also that the “faces” and “stickers” of the puzzle are separated from each other by gaps. In a real 4D magic cube (if that makes any sense), all the “faces” and “stickers” would be slammed together. The view we present is simply an exploded version of the real 4D puzzle so that you can see the internal state. It is a good idea to imagine how they would slam together, because adjacent “stickers” on adjacent “faces” are permanently stuck together just like pairs and triplets of stickers on the original 3D magic cube are permanently stuck together on the outer 26 plastic parts.