Authors: J Gregory Moxness
It is widely known that the E8 polytope can be folded into two Golden Ratio (Phi) scaled copies of the 4 dimensional (4D) 120 vertex 720 edge H4 600-cell. While folding an 8D object into a 4D one is done by applying the dot product of each vertex to a 4x8 folding matrix, we use an 8x8 rotation matrix to produce four 4D copies of H4 600-cells, with the original two left side scaled 4D copies related to the two right side 4D copies in a very specific way. This paper will describe and visualize in detail the specific symmetry relationships which emerge from that rotation of E8 and the emergent fourfold copies of H4. It will also introduce a projection basis using the Icosahedron found within the 8x8 rotation matrix. It will complete the detail for constructing E8 from the 3D Platonic solids, Icosians, and the 4D H4 600-cell. Eight pairs of Phi scaled concentric Platonic solids are identified directly using the sorted and grouped 3D projected vertex norms present within E8.
Comments: 18 Pages.
[v1] 2018-08-08 11:39:58
Unique-IP document downloads: 85 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.