E8 Projected to the Concentric Hulls of H4+H4 Phi

The 8 concentric projected 3D hulls from the vertices of the 4_21 polytope (using the split real even E8 roots) and a projection basis from 3 of the 4 rows of the E8 to the H4+H4 Phi folding matrix produce from inner to outer (sorted by vertex Norm):

  • 4 Points at the origin
  • 2 Icosahedron
  • 2 Dodecaheron
  • 4 Icosahedron
  • 1 Icosadodecahedron
  • 2 Dodecaheron
  • 2 Icosahedron
  • 1 Icosadodecahedron

Projection Basis:

Looking at it as an orthonormal 3D projection of 2 600-cells (from the fully folded E8 to H4+H4 Phi), which is the same (as it should be), but rotated.

Here is just one 600-cell (interior).

Here is E7 doing the same procedure:

And again for E6

Wow – that is nice! Remember, you heard it here first!

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. 

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