Icosahedral Symmetry and the Golden Ratio in Viral Capsid Geometry — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Icosahedral symmetry is the dominant structural motif in viral capsids, enabling efficient self-assembly and genome protection. | MATH: Icosahedral symmetry group \( I_h \) (order 120); capsid geometry described by Caspar-Klug theory using triangulation number \( T = h^2 + hk + k^2 \), where \( h, k \) are non-negative integers (e.g., \( T=1,3,4,7,... \)). | CONNECTION: Icosahedral symmetry directly embeds golden ratio \( \varphi = (1+\sqrt{5})/2 \approx 1.618 \); coordinates of icosahedron vertices involve \( 0, \pm1, \pm\varphi \); dihedral angles yield ratios \( 0.618 \) (1/φ) and \( 2.618 \) (φ²). The \( T \)-number lattice is a hexagonal tiling in the plane, linked to base-60 via 60° rotational symmetry. | DEPTH: 8 — This is a profound geometric constraint: viruses exploit the most efficient spherical packing symmetry (icosahedral) to maximize volume-to-surface ratio, minimize genetic material, and enable error-free self-assembly. The Caspar-Klug classification is a direc 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: W7203708170
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