The same 3 (projection basis vectors that produce the H3 Icosadodecahedron from D6 and the Rhombic Triacontahedron from the 6-Cube (or 2 sets from the 128 1/2 Integer BC8 vertices of E8) form lower dimensional objects within E8.

For more information on the above symmetries, see this post.

The 3D object identification has been confirmed by …

32 vertex 5-Cube with 80 5D Norm’d Unit Length Edges
Projection Basis Vectors {x,y,z}:

Projected Vertex Data:

3D Rhombic 20-Hedron Outer Hull of 22 Vertices

The edge coloring on these projections are defined by which of the 6 dimensional axis the edge aligns with.

10 Interrior Vertices with 10 Edges

All Vertices in 3D

2D faces

16 vertex 4-Cube with 32 4D Norm’d Unit Length Edges
Projection Basis Vectors {x,y,z}:

Projected Vertex Data:

3D Rhombic Dodecahedron with 2 Interior Vertices

2D faces

BTW – if you find this information useful, or provide any portion of it to others, PLEASE make sure you cite this post. If you feel a blog post citation would not be an acceptable form for academic research papers, I would be glad to clean it up and put it into LaTex format in order to provide it to arXiv (with your academic sponsorship) or Vixra. Just send me a note at:  jgmoxness@theoryofeverthing.org.