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 Tom Ruen.
3D Rhombic 20-Hedron Outer Hull of 22 Vertices
3D Rhombic Dodecahedron with 2 Interior Vertices
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