E8, H4, Quasi-Crystals, Penrose Tiling, Boerdijk-Coxeter Helices and an AMS blog post on the topic

This pic is an overlay of an image from Greg Egan on the AMS blog VisualInsight on top of one I created several years ago for the quasicrystal wikipedia page.

It uses my E8-H4 folding matrix to project E8 vertices to several interesting objects. The 5 dimensional 5-cube (Penteract) and the related 3D the Rhombic-Triacontahedron, as well as this 2D overlay on the Ho-Mg-Zn electron diffraction pattern.


E8 vertices projected to 2D pentagonal projection

5-cube in 3D

6-cube edges projected to the Rhombic-Triacontahedron using 3 of 4 rows of my E8-H4 folding matrix.

Rhombic-Triacontahedron with inner edges removed

The Boerdijk-Coxeter helix is also related to these structures through the Golden Ratio.

Edges on the outer ring of the E8 Petrie projection related to Boerdijk-Coxeter helix.

Same as above in 3D with the tetrahedral cell faces and 3D vertex shape-color-size based on quantum particle parameters from a theoretical physics model.

Same as above also showing the inner E8 ring Boerdijk-Coxeter helix.
Platonic solids

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