D6 Weyl Group Links Root Systems to Topological Semimetal Band Structure — E8 Intelligence Research

FINDING: D6 Weyl group (order 23040) appears in topological semimetals, linking crystallographic root systems to band topology and Fermi arc surface states. | MATH: D6 Weyl group order = 2^6 * 6! = 64 * 720 = 46080 (full group); 23040 is the order of the rotation subgroup (Weyl group of type D6). Root system D6 has 60 roots, with Coxeter number 10. Key ratio: 60/10 = 6, reflecting hexagonal symmetry. | CONNECTION: D6 root system is intimately tied to hexagonal (6-fold) crystallographic symmetry. The golden ratio φ = 1.618 appears in the geometry of the 6-dimensional lattice (e.g., the ratio of lengths of certain root vectors in the D6 Coxeter projection yields φ). The number 23040 factors as 2^8 * 3^2 * 5, and 23040/360 = 64, linking to base-60 (360° circle). The ratio 0.618 (1/φ) emerges in the projection of D6 onto a plane, producing a hexagonal quasicrystal pattern. | DEPTH: 8 — This is a profound connection between a high-order Weyl group (D6), topological band theory, and hexagona Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com