English: The E8 4_21 polytope is projected to 3D using 3 rows of the E8 to H4 folding matrix giving H3 symmetry. The vertices are sorted and tallied by their 3D norm. Generating the increasingly transparent hull of each set of tallied norms shows:

1) 4 points at the origin
2) 2 icosahedrons
3) 2 dodecahedrons
4) 4 icosahedrons
5) 1 icosadodecahedron
6) 2 dodecahedrons
7) 2 icosahedrons
8) 1 icosadodecahedron

for a total of 240 vertices. This is, of course, 2 concentric sets of hulls from the H4 symmetry of the w:600-cell scaled by the golden ratio. For more information, see my blog post here. [1]