The first polytope has 5-cells, 8-cells, 16-cells, 24-cells. Polytopes are 4-D and all have a fourth axis. They all have have to rotate consistantly for it show all of its faces, but we can't currently create and actual polytope because the Macro Verses we know is 3-D, but we can only see its plane or cross section. It is much easier to represent a polytope with computers on 2-D screens because if we tried to represent it with three dimensions all we can see is its hyperplane: 3-D used to represent a dimension higher than three. The hyperplane of an Polytope is seen as cross section of it in the Macro verse. (less info)