Golden Ratio Links Rhombic Dodecahedron and Icosidodecahedron via Radial Expansion — E8 Intelligence Research

FINDING: Rhombic dodecahedron and icosidodecahedron are linked via radial expansion, with the golden ratio governing edge-length ratios and face angles (arccos(−1/3) for the rhombic dodecahedron's acute angle). | MATH: Rhombic dodecahedron face angles: acute = arccos(1/3) ≈ 70.53°, obtuse = 180° − 70.53° = 109.47° = arccos(−1/3). Edge length of rhombic dodecahedron (from cube of side a): \( \frac{\sqrt{3}}{2}a \). Icosidodecahedron: 30 vertices, 20 triangles + 12 pentagons; its circumradius R = φ·(edge length) where φ = (1+√5)/2 ≈ 1.618. Radial expansion ratio between the two polyhedra (if sharing a common circumsphere) is φ² = 2.618 or φ, depending on orientation — the videos show periodic packing, implying a scaling factor of φ per radial step. | CONNECTION: The rhombic dodecahedron is the Voronoi cell of the face-centered cubic (FCC) lattice — a root lattice of type A₃ (or D₃). The icosidodecahedron is the Archimedean solid with full icosahedral symmetry (H₃ Coxeter group). Their ra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com