Icosahedral Symmetry Constraints on Viral Capsid Structure via Caspar-Klug T-Numbers — E8 Intelligence Research

FINDING: Viral capsid T-number theory reveals that spherical viruses are constrained to specific triangulation numbers T = h² + hk + k², where h,k are non-negative integers, enforcing icosahedral symmetry. MATH: T = h² + hk + k²; number of capsid proteins = 60T; allowed T values: 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36, 37, 39, 43, 48, 49, ... (Caspar-Klug classification). Icosahedral symmetry group order = 60. CONNECTION: T-number sequence is deeply linked to hexagonal lattice geometry and the Eisenstein integers (complex numbers of form a + bω, ω = e2πi/3). The ratio of successive T numbers often approaches 1.618 (golden ratio) asymptotically. The allowed T values correspond to points in a triangular lattice, reflecting the underlying hexagonal close-packing and the 5-fold symmetry of icosahedra. The golden ratio φ = (1+√5)/2 ≈ 1.618 appears in the geometry of the icosahedron (edge/radius ratio). Base-60 connections: 60T proteins per capsid; 60 is a highly composit Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com