Dimensional Cube

If you took a look at this, what would you say it was? My professor in Computer Science brought this up. We hear of 2d boxes that have 4(2^2[2d]) verticies. If we wanted to make a cube, we would make another axis and through some complicated copying of the previous image, the cube would have 8(2^3[3d]) verticies. Now my Professor said that we could do the same thing in 4d; this means that there would be 16 verticies. I thought it was the craziest illusion ever. Try googling 4d cube.