Rotating Hypercube

The object you see is the four-dimensional analog of a cube, just like a cube is a three-dimensional analog of a square. As you watch this video, realize there are no cubes on the "inside." The cubes you see are the outside of the shape just as squares are the outside of a cube. Look at the perspective drawings of a cube below. In the one on the right the smaller square is NOT "inside" the cube. It's just a matter of perspective, as if you are looking into a box, and the back is farther away than the front. Same thing with this video. The hypercube is ROTATING. It is NOT turning itself inside out.