More Symmetries of E8 folding, including 5-Cube and 4-Cube (Tesseract)

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.

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. 

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