The Rhombic Enneacontahedron: A 15-Zone Zonohedron from Icosahedral Symmetry — E8 Intelligence Research

FINDING: The rhombic enneacontahedron is a 15-zone zonohedron whose 90 faces arise from the 15 axes of the icosahedral symmetry group (A₅), constructible via Zometool's 10-axis hub and dual to a near-miss Johnson solid. | MATH: Zonohedron with 15 zone axes → n(n−1) = 15×14 = 210 face pairs, but icosahedral symmetry reduces to 90 rhombic faces (30 of one type, 60 of another). Face angles: acute ≈ 43.68° and 76.34° (from golden ratio: tan⁻¹(φ) and related), obtuse supplements. Edge lengths equal (unit rhombi). Dual has 32 vertices (12+20) — icosahedron + dodecahedron vertex counts. | CONNECTION: Directly encodes the 15 great circles of the icosahedron (15 zone axes = 15 pairs of opposite edges of the icosahedron). The rhombi's acute angles relate to φ: cos⁻¹(1/√5) ≈ 63.43° and cos⁻¹(√5/3) ≈ 41.81° — both expressible via φ = (1+√5)/2. The 10 Zometool hub axes correspond to the 10 3-fold axes of the icosahedral group (A₅), which is the symmetry of the 600-cell and the E₈ root system's Coxe Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com