Icosahedral Symmetry and Quasi-Equivalence: The Mathematical Architecture of Viral Capsids — E8 Intelligence Research

Abstract

FINDING: Icosahedral symmetry is the dominant architectural principle in viral capsid structure, governed by quasi-equivalence theory. | MATH: Icosahedral group I_h (order 120); 5-3-2 rotational symmetry axes; Caspar-Klug triangulation number T = h² + hk + k² (h,k ≥ 0 integers), yielding T = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 37, 43, 49, 57, 63, 64, 75, 76, 81, 84, 91, 93, 97, 108, 112, 121, 124, 127, 129, 133, 139, 147, 148, 151, 156, 157, 163, 169, 171, 175, 181, 183, 189, 192, 193, 196, 199... (T = 60T protein subunits); golden ratio φ = (1+√5)/2 ≈ 1.618 appears in icosahedron vertex coordinates (0, ±1, ±φ), (±1, ±φ, 0), (±φ, 0, ±1). | CONNECTION: Icosahedral symmetry is the crystallographic point group of the 6D root system D_6 (the "hexagonal" lattice in 6D projected to 3D); the golden ratio φ is intrinsic to the icosahedron's geometry — its 12 vertices form 3 mutually orthogonal golden rectangles. The dihedral angle of the icosahedron is arccos(-√5/3) ≈ 138.19°, a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com