FINDING: E8 lattice projected onto H3 Coxeter plane yields 3D icosahedral quasicrystal diffraction patterns; solidification model uses quaternion order parameter linking E8 to 3D quasicrystal formation. MATH: - E8 root system: 240 minimal vectors in 8D; 6720 edges in Gosset 4₂1 polytope. - H3 Coxeter plane projection: reduces 8D to 3D, preserving icosahedral symmetry (H3 group order 120). - Quaternion orientational order parameter: \ (Q = ₈ qᵢ qᵢ^* \) (rank-1 tensor in 4D quaternion space), with critical exponents from E8 lattice formation. - Key ratios in quasicrystal diffraction: golden ratio \ (= (1+5) /2 1. 618\), its inverse \ (1/ 0. 618\), and \ (² 2. 618\) appear in vertex positions and Fourier peaks. CONNECTION: - Icosahedral symmetry (H3) is a subgroup of E8 (Weyl group order 696729600). - Projection yields 3D Penrose tiling with inflation factor \ (³ 4. 236\). - Quaternion order parameter natur Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com
Andrew Stewart Caldin (Wed,) studied this question.