I've noticed in this wikipedia article that each 4D figure is constructed of 3D platonic solids to get to these, just like using polygons on solids. In the hypercube, you have the cube in the center and the cube on the outside. The cube rotates oddly, allowing there to be 4 positions with this. and then using simple math, you get $4\times 2=8$, and there are 8 cubes in a hypercube net, seen at the aforementioned first link.
But there is something off: I can't see how the 3D animations of the 5-cell, 120-cell, and 600-cell rotate so i cannot distinguish the 5 or 120 or 600 figures. Is there another way (besides the nets) to tell that the 600-cell has 600 tetrahedron?