Molecular Platonic Solids Realized via Finite Coxeter Groups Including Non-Crystallographic Icosahedral H3 — E8 Intelligence Research

FINDING: Platonic solids are realized in molecular chemistry via finite Coxeter groups (A3, B3, H3), with non-crystallographic H3 (icosahedral) appearing in actual molecules, bridging discrete geometry and chemical structure. | MATH: Coxeter groups: A3 (tetrahedron, order 24), B3 (octahedron/cube, order 48), H3 (icosahedron/dodecahedron, order 120). Euler characteristic: V−E+F=2. Duality: tetrahedron self-dual; cube↔octahedron; dodecahedron↔icosahedron. Non-crystallographic constraint: H3 lacks invariant lattice under reflection (no 5-fold translational symmetry). | CONNECTION: H3 contains golden ratio φ=1.618 and its inverse 0.618 in edge ratios of icosahedron/dodecahedron; dihedral angles yield 0.786 (cos⁻¹(1/√5) related) and 2.618=φ² appears in icosahedral vertex coordinates. Base-60 not directly implicated, but 5-fold symmetry (pentagon) ties to Babylonian sexagesimal fractions (1/5=0.2, 1/3=0.333 in base-60). | DEPTH: 7 — solid mathematical grounding (Coxeter classification) but f Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com