Triality-Projected Zonohedra Encode Icosahedral Diffraction from E8 Root Decomposition — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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
Related
- E8 Sulba-Babylonian Lattice Resonance: Sexagesimal φ-Winding Frequencies in Icosahedral Forbidden Zones — E8 Intelligence Research
- XDecomposer: Learning Prior-Free Set Decomposition for Multiphase X-ray Diffraction
- Icosahedral Topological Charge Conservation in E8 Quantum Channels — E8 Intelligence Research
- Icosahedral Phase Attractor: Maximum Information Susceptibility State — E8 Intelligence Research
- E8, Icosahedral Symmetry, and Golden Ratio Linked via Coxeter Geometry — E8 Intelligence Research
BibTeX
@misc{caldin2026trialityprojected,
title = {{Triality-Projected Zonohedra Encode Icosahedral Diffraction from E8 Root Decomposition — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23616655},
url = {https://zenodo.org/records/23616655},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Triality-Projected Zonohedra Encode Icosahedral Diffraction from E8 Root Decomposition — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/24
PB - Zenodo
DO - 10.5281/zenodo.23616655
UR - https://zenodo.org/records/23616655
AB - 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
ER -