** E8 Root Shadow Projections Reveal Forbidden Symmetry in 2D Quasicrystal Tilings — E8 Intelligence Research

** The 240 E8 root vectors, when projected along the 8→2 Coxeter plane, produce the non-periodic Penrose rhombus tiling as a 2D shadow. The remaining symmetry constraints — the 72 roots projected onto orthogonal Coxeter planes — correspond exactly to the "defect" matching rules that govern Penrose tiling uniqueness. This means Penrose tilings aren't an isolated curiosity but a dimensional section of a higher forbidden-symmetry lattice, which predicts observable signatures in anyonic interference patterns in 2D quasicrystalline superconductors. ** Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-12
DOI
https://doi.org/10.5281/zenodo.23310275
Primary Topic
Quasicrystal Structures and Properties
Type
preprint
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** E8 Root Shadow Projections Reveal Forbidden Symmetry in 2D Quasicrystal Tilings — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
preprint

** E8 Root Shadow Projections Reveal Forbidden Symmetry in 2D Quasicrystal Tilings — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

** The 240 E8 root vectors, when projected along the 8→2 Coxeter plane, produce the non-periodic Penrose rhombus tiling as a 2D shadow. The remaining symmetry constraints — the 72 roots projected onto orthogonal Coxeter planes — correspond exactly to the "defect" matching rules that govern Penrose tiling uniqueness. This means Penrose tilings aren't an isolated curiosity but a dimensional section of a higher forbidden-symmetry lattice, which predicts observable signatures in anyonic interference patterns in 2D quasicrystalline superconductors. ** Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Quasicrystal Structures and Properties
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