Icosahedral Symmetry and Quasi-Equivalence: The Triangulation Number Determines Viral Capsid Architecture — E8 Intelligence Research

FINDING: Viral capsid architecture is governed by icosahedral symmetry and quasi-equivalence theory, where the triangulation number T = h² + hk + k² (h,k ≥ 0 integers) determines the number of protein subunits (60T) and their arrangement on a spherical lattice. | MATH: T = h² + hk + k²; capsid protein count = 60T; 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, 63, 64, 67, 73, 75, 76, 79, 81, 84, 91, 93, 97, 100, … (integers of form h²+hk+k²); icosahedral rotation group A₅ (order 60) acts on the capsid; quasi-equivalence allows slight conformational variation of identical protein subunits to fit non-equivalent lattice positions. | CONNECTION: The T-number lattice is a hexagonal lattice (root system A₂) projected onto the icosahedron — the same lattice that generates the golden ratio φ = (1+√5)/2 ≈ 1.618 via its basis vectors (1,0) and (1/2, √3/2). The 60-fold symmetry directly encodes the 60° base-60 angle structure (hexagonal tiling Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com