Fibonacci Chain Spacing Links 6D Hypercubic Lattice to 3D Icosahedral Quasicrystal — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Cut-and-project from 6D hypercubic lattice to 3D icosahedral quasicrystal uses Fibonacci chain plane spacing, linking 6D periodicity to 3D aperiodic order. | MATH: 6D hypercubic lattice → 3D projection via irrational slope (golden ratio φ = (1+√5)/2 ≈ 1.618). Fibonacci chain spacing: successive intervals follow Fibonacci numbers F_n, ratio F_{n+1}/F_n → φ. Key constants: φ, 1/φ ≈ 0.618, φ² ≈ 2.618. Penrose tiling vertices from 5D de Bruijn method; 3D icosahedral quasicrystal from 6D. | CONNECTION: Golden ratio φ (1.618) and its inverse 0.618 govern plane spacings. Icosahedral symmetry (5-fold, 3-fold, 2-fold axes) from 6D cubic lattice. Rhombic hexecontahedron (30 rhombi, 32 vertices) emerges as star-burst shape. | DEPTH: 8 — Directly ties 6D lattice to 3D quasicrystal via φ, unifying periodicity and aperiodicity through cut-and-project, a profound geometric harmony. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170477665
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