English: An alternate 120-Cell with unit circumradius in vertex up coordinates showing the individual 16 concentric hulls and in combination. Orthogonal projection of the 120-cell using any 3 of these Cartesian coordinate dimensions forms an outer hull with 10 decagon and 60 pentagon faces, an as-yet unnamed solid.

Hull 1 has 2 points at the origin.
Hulls 2 & 6 are cubes.
Hulls 3 & 5 are rhombicuboctahedrons.
Hulls 4 & 12 are each pairs of truncated octahedrons.
Hulls 7 & 15 are truncated cuboctahedrons.
Hull 11 is a truncated cube.
Hulls 8, 9, 10, 13, 14, and 16 are unnamed solids.

This is constructed from VisibLie_E8 found on TheoryOfEverything.org.

Here [1] is a link to a Powerpoint presentation that shows the generation of all 3D Platonic, Archimedean and Catalan solids, as well as the popular 4D polychora using quaternion Weyl orbits from Coxeter-Dynkin ​Geometric Group Theory concepts. The first 8 slides introduce the material and my interactive demonstration, slides 9-28 review the Coxeter-Dynkin group theory with Hasse diagrams, and slides 29-48 show the 3D solid orbit generation, with slide 49-62 showing the 4D polychora with links to the higher dimensions of E8.