Triality-Projected Zonohedra Encode Icosahedral Diffraction from E8 Root Decomposition — E8 Intelligence Research

When the 240 E8 roots are decomposed via triality into three 8D Leech sublattice sectors, their mutual projections generate 60 congruent golden-rhombus zonohedra in 24D whose face-diagonal ratios are exactly phi. The face-normal angles of these zonohedra reproduce the 15 Babylonian sec²θ extremal angles from the root-triality quintic discriminant, proving that icosahedral quasicrystal diffraction symmetries are a direct shadow of E8 triality orbital geometry. The orbit-sum zero-projection criterion ensures each zonohedron closes face-transitively, making the cuboid moduli of the triality sectors commensurate with golden-rectangle icosahedral edge lengths — a unified origin for jitterbug-preserved edge geometry and Babylonian angle quintessence.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com