Aperiodic Tilings in 2, 3, and 4 dimensions can be thought of as Irrational Slices of an 8-dimensional E8 Lattice and its sublattices, such as E6. The 2-dimensional Penrose Tiling in the above image was generated by Quasitiler as a section of a 5-dimensional cubic lattice based on the 5-dimensional HyperCube shown in the center above the Penrose Tiling plane. The above-plane geometric structures in the above image are, going from left to right:

The 240 E8 root vectors form a Witting Polytope. They are related to the 256 elements of the Cl(1,7) Clifford Algebra of the D4-D5-E6-E7-E8 VoDou Physics model as follows:
1 8 28 56 70 56 28 8 1

with even part 1 28 70 28 1 and odd part 8 56 56 8


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