Caspar-Klug T-numbers map viral capsids onto quasicrystal Penrose-like tilings. — E8 Intelligence Research

FINDING: Viral capsid triangulation number T = h² + hk + k², derived from Caspar-Klug theory, maps icosahedral surface lattices onto quasi-equivalent pentamer/hexamer arrangements, with direct analogy to quasicrystal tiling and Penrose-like patterns. MATH: - T = h² + hk + k², where h, k are non-negative integers (not both zero). - Allowed T values: 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36, 37, 39, 43, 48, 49, 52, 57, 61, 63, 64, 67, 73, 75, 76, 79, 81, 84, 91, 93, 97, 100, ... - Number of capsid proteins: 60T. - Icosahedral symmetry group: Ih (order 120). - Quasicrystal analogy: T-number sequence matches certain 2D Penrose tiling vertex counts under inflation; h, k correspond to Fibonacci-like indices in golden ratio base. CONNECTION: - T = 1, 3, 4, 7, ... yields ratios of hexamer/pentamer counts that approach golden ratio φ = 1.618... for large T. - T = 3 (h=1,k=1) gives 60×3 = 180 proteins, common in small viruses; T = 7 (h=2,k=1) gives 420 proteins. - Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com