Octagonal Quasicrystals: Silver Ratio, E8 Symmetry, and Quantum Transport — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Octagonal quasicrystal design based on Ammann-Beenker tiling with patchy particles, linking silver ratio to quantum transport and Higgs mass via E8 symmetry. MATH: Silver ratio δ_s = 1 + √2 ≈ 2.414; its reciprocal 1/δ_s ≈ 0.414; Ammann-Beenker tiling uses 8-fold rotational symmetry; E8 root system has 240 roots, Coxeter number 30, and is linked to silver ratio via non-crystallographic projections. CONNECTION: Octagonal quasicrystals exhibit 8-fold symmetry (crystallographically forbidden in periodic crystals), directly tied to silver ratio (δ_s = 1:√2 ratio). The E8 silver ratio connection to Higgs mass (≈125 GeV) suggests a geometric mass formula: m_H ∝ δ_s * (some scale). Base-60 not evident, but 8-fold symmetry relates to √2 and silver mean family. DEPTH: 7 — Strong geometric link between quasicrystal structure (Ammann-Beenker) and silver ratio, with speculative but mathematically coherent E8-Higgs mass relation. The patchy-particle realization is a concrete step towa Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170669148
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