Icosahedral Symmetry and Quasi-Equivalence: The Mathematical Blueprint of Viral Capsid Architecture — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Icosahedral symmetry dominates viral capsid architecture, with quasi-equivalence theory explaining how identical protein subunits assemble into 60n-valence shells. | MATH: Icosahedral group I_h (order 120); capsid triangulation number T = h² + hk + k² (Caspar-Klug), yielding T = 1, 3, 4, 7, 9, 13, 16, 19, 21...; subunit count = 60T; the golden ratio φ = (1+√5)/2 ≈ 1.618 appears intrinsically in the icosahedron's vertex coordinates (0, ±1, ±φ) and in its dihedral angles (arccos(-1/√5) ≈ 116.565°). | CONNECTION: The icosahedron is the dual of the dodecahedron — both encode φ³ = 2+√5 ≈ 4.236 and φ⁻¹ = 0.618 in their geometry. The T-number lattice is a hexagonal (base-60-compatible) lattice on the icosahedral surface, directly linking to crystallographic root system H₃ (non-crystallographic, but with 2,3,5-fold symmetries). The ratio 0.382 = 1/φ² appears in the relative radii of icosahedral shells (inner/outer capsid layers). | DEPTH: 8/10 — This is a profound, experimentally veri 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: W7221453128
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