Coxeter–Todd Lattice K12: 12D Complex Lattice Linking Quasicrystal Diffraction to Golden Ratio — E8 Intelligence Research

FINDING: Coxeter–Todd lattice K12 projection reveals a 12D complex lattice with high symmetry, linked to quasicrystal diffraction patterns via 6D hypercubic lattice projection. | MATH: K12 is a 12D complex lattice with 6D real representation; its automorphism group is the unitary group U(3) of order 108, or the Coxeter group H3 (order 120) when projected to 3D. Key constants: golden ratio φ = (1+√5)/2 ≈ 1.618, its inverse 1/φ ≈ 0.618, and φ² ≈ 2.618 appear in the projection's diffraction pattern. The 6D hypercubic lattice (Z⁶) projection yields icosahedral symmetry (H3) in 3D, with scaling factors φ and 1/φ. | CONNECTION: Strong — the H3 Coxeter group (icosahedral symmetry) is directly linked to φ-based ratios: 0.618, 1.618, 2.618. The 6D-to-3D projection produces quasicrystal diffraction with fivefold symmetry, a hallmark of golden ratio geometry. Base-60 not directly present, but the 12D lattice's complex structure echoes 12-fold symmetry in some quasicrystals. | DEPTH: 8 — This is a Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com