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.
![Ho-Mg-Zn_E8-5Cube-baez-egan-overlay](http://theoryofeverything.org/MyToE/wp-content/uploads/2015/02/Ho-Mg-Zn_E8-5Cube-baez-egan-overlay.png)
E8 vertices projected to 2D pentagonal projection
![E8-5Cube](http://theoryofeverything.org/MyToE/wp-content/uploads/2015/02/E8-5Cube.jpg)
5-cube in 3D
![5-cube-2](http://theoryofeverything.org/MyToE/wp-content/uploads/2015/02/5-cube-2.png)
6-cube edges projected to the Rhombic-Triacontahedron using 3 of 4 rows of my E8-H4 folding matrix.
![6Cube-QuasiCrystal-low](http://theoryofeverything.org/MyToE/wp-content/uploads/2015/02/6Cube-QuasiCrystal-low.jpg)
Rhombic-Triacontahedron with inner edges removed
![RhombicTricontahedron](http://theoryofeverything.org/MyToE/wp-content/uploads/2015/02/RhombicTricontahedron.png)
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.
![helix2Db](http://theoryofeverything.org/MyToE/wp-content/uploads/2015/02/helix2Db.png)
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.
![cells6004b](http://theoryofeverything.org/MyToE/wp-content/uploads/2015/02/cells6004b.png)
Same as above also showing the inner E8 ring Boerdijk-Coxeter helix.
![inner-outerP](http://theoryofeverything.org/MyToE/wp-content/uploads/2015/02/inner-outerP.png)
Platonic solids
![E8-3D-Platonic-2](http://theoryofeverything.org/MyToE/wp-content/uploads/2014/11/E8-3D-Platonic-2.png)