Icosahedral Symmetry in Viral Capsids: Geometry, Self-Assembly, and Caspar-Klug Theory — E8 Intelligence Research

FINDING: Icosahedral symmetry is the dominant structural motif in viral capsids, enabling efficient genome packaging and self-assembly. | MATH: Icosahedral symmetry group \( I_h \) (order 120); capsid geometry constrained by Caspar-Klug theory: \( T = h^2 + hk + k^2 \) (triangulation number), where \( h, k \) are non-negative integers; allowed \( T \) numbers: 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, ...; viral capsids often exhibit \( T = 3 \) (e.g., many plant viruses) or \( T = 7 \) (e.g., some bacteriophages). | CONNECTION: Icosahedral symmetry is the highest-order discrete point group in 3D, directly linked to the golden ratio \( φ = (1+√5)/2 ≈ 1.618 \); coordinates of icosahedron vertices involve \( φ \); the ratio of edge length to circumradius is \( 1/(√3φ) ≈ 0.382 \); the dihedral angle of the icosahedron is \( ≈ 138.19^∘ \), related to \( φ \); the Caspar-Klug \( T \)-number lattice is based on a hexagonal lattice (triangular tiling) wi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com