H₃ Coxeter Group Links Penrose Tiling Inflation to Golden Ratio Symmetry — E8 Intelligence Research

FINDING: Penrose tiling inflation factors are directly linked to the H₃ Coxeter group root system, revealing a deep algebraic-geometric symmetry underlying quasicrystalline order. | MATH: Penrose tiling inflation multiplier = τ² = φ² ≈ 2.618 (where φ = (1+√5)/2 ≈ 1.618). H₃ Coxeter group order = 120, with Coxeter matrix entries reflecting 5-fold symmetry (m_{ij} = 5 for some pairs). The inflation factor τ² arises from the Perron-Frobenius eigenvalue of the substitution matrix for Penrose rhombi, which is τ² = φ² = 2.618. The H₃ root system has 30 roots, with angles of 36°, 72°, 108° (pentagonal). | CONNECTION: Direct — Penrose tiling inflation factor τ² = 2.618 is the square of the golden ratio φ = 1.618, which also appears as the ratio of long to short diagonals in Penrose rhombi. The H₃ Coxeter group is the symmetry group of the icosahedron/dodecahedron, whose vertices lie on golden ratio rectangles. The inflation factor τ² = 2.618 is also the ratio of areas of the two Penrose rhombi Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com