A₅ Symmetry and Golden Ratio Unify Icosahedral Lepton Mixing — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Icosahedral symmetry (A₅) is a simple group, dual to dodecahedron, generated by three mutually orthogonal golden rectangles; its lepton-mixing predictions tie A₅ to the golden ratio. | MATH: A₅ ≅ rotational icosahedral group, |A₅| = 60, simple (no nontrivial normal subgroups). Golden ratio φ = (1+√5)/2 ≈ 1.618; its conjugate φ⁻¹ = (√5−1)/2 ≈ 0.618. Three golden rectangles (aspect φ:1) intersect orthogonally to define the 12 vertices of the icosahedron. Dodecahedron–icosahedron duality: V_ico = 12, F_ico = 20, E = 30; dual swaps V↔F. Solar neutrino mixing angles predicted via A₅ family symmetry yield sin²θ₁₂ ≈ 1/(2+φ) ≈ 0.276 (or related golden-ratio expressions) — see arXiv:0812.1057. | CONNECTION: Golden ratio φ and φ⁻¹ appear as the fundamental edge/vertex ratios; A₅ is the symmetry of the icosahedron, whose Coxeter–Dynkin diagram H₃ has edge labels 5 (φ-related). The icosahedron's 6 fivefold axes correspond to 6 golden rectangles; 10 threefold axes, 15 twofold axes — these
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026a₅,
title = {{A₅ Symmetry and Golden Ratio Unify Icosahedral Lepton Mixing — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23446591},
url = {https://zenodo.org/records/23446591},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A₅ Symmetry and Golden Ratio Unify Icosahedral Lepton Mixing — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23446591
UR - https://zenodo.org/records/23446591
AB - FINDING: Icosahedral symmetry (A₅) is a simple group, dual to dodecahedron, generated by three mutually orthogonal golden rectangles; its lepton-mixing predictions tie A₅ to the golden ratio. | MATH: A₅ ≅ rotational icosahedral group, |A₅| = 60, simple (no nontrivial normal subgroups). Golden ratio φ = (1+√5)/2 ≈ 1.618; its conjugate φ⁻¹ = (√5−1)/2 ≈ 0.618. Three golden rectangles (aspect φ:1) intersect orthogonally to define the 12 vertices of the icosahedron. Dodecahedron–icosahedron duality: V_ico = 12, F_ico = 20, E = 30; dual swaps V↔F. Solar neutrino mixing angles predicted via A₅ family symmetry yield sin²θ₁₂ ≈ 1/(2+φ) ≈ 0.276 (or related golden-ratio expressions) — see arXiv:0812.1057. | CONNECTION: Golden ratio φ and φ⁻¹ appear as the fundamental edge/vertex ratios; A₅ is the symmetry of the icosahedron, whose Coxeter–Dynkin diagram H₃ has edge labels 5 (φ-related). The icosahedron's 6 fivefold axes correspond to 6 golden rectangles; 10 threefold axes, 15 twofold axes — these Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -