Quaternion Orbits of W(H4) Generate Polytopes with Icosahedral 3D Projections — E8 Intelligence Research

FINDING: H4 polytopes and their duals are constructed as quaternion orbits of the Coxeter-Weyl group W(H4), with 3D projections preserving icosahedral symmetry. | MATH: W(H4) group elements and vertices represented by quaternions; orbits generate polytopes and their duals; projection to 3D retains icosahedral (H3) symmetry. | CONNECTION: H4 root system contains golden ratio φ = (1+√5)/2 ≈ 1.618; its dual polytope scaling involves φ² ≈ 2.618; icosahedral symmetry (H3) is a subgroup of H4, linking 4D to 3D golden-ratio-based structures. | DEPTH: 8 — Directly ties quaternion algebra, Coxeter groups, and golden ratio scaling in 4D polytopes, with explicit dual relationships and symmetry breaking to 3D icosahedral lattices. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com