These images are created from VisibLie_E8, a free interactive Mathematica Computable Document Format (CDF) program at:
This is also available as a full notebook for those with Mathematica licenses for exporting to 2D, 3D and 4D (time animation) formats.
E8 Laser Etched Crystal
This is a photo of a 3D projection of E8 saved as a Stereo Lithography (.stl) file and laser etched into a 3” jewel cut optical crystal. It sits on a multicolored LED light base to produce the coloring effects. Each vertex of E8 has a shape and size according to a theoretical assignment of fundamental physics particles by A. G. Lisi.
E8 folded to the 600 Cell
This is the Petrie projection of the 600 Cell. E8 is “folded” into the Coxeter-Dynkin H4 a. k. a. the 120 vertex 600 Cell using the Golden Ratio (Phi).
A 3D print with titanium of a 4D 120 Cell projected into 3 space. E8 can be “folded” into two 4D objects, the Coxeter-Dynkin H4+H4/Phi (Phi=Golden Ratio, and H4 is a. k. a. the 120 vertex 600 Cell). The dual of the 600 Cell is the 600 vertex 120 Cell, shown here in a perspective projection.
E8 and the 6 Cube Hexeract
E8 contains a 6 Cube (a. k. a. Hexeract), which is projected using a perspective projection. The number of overlapping vertices in the projection are indicated by colors.
E8 and the Rhombic Triacontahedron
E8 contains a 6-cube (Hexeract), which can be orthographically projected to 3D using the Golden ratio. This is used to understand the aperiodic icosahedral structure of Quasicrystals. Its outer hull of vertices and edges form the Rhombic Triacontahedron, which contains the Platonic solids including the Dodecahedron and Icosahedron.
E8 on QuasiCrystal Electron Diffraction
240 E8 polytope vertices projected to 2D using 5-cube Petrie basis vectors overlaid on electron diffraction pattern of an icosahedral Zn-Mg-Ho Quasicrystal. The number of overlapping vertices in the projection are indicated by colors.