Golden Isozonohedra from Icosidodecahedra: A Geometric Link to FCC Lattice — E8 Intelligence Research
FINDING: Golden isozonohedra (all faces golden rhombi) constructible from icosidodecahedra, linking to FCC lattice via rhombic dodecahedron; hexaquark decay analysis is unrelated to geometry. MATH: Golden rhombus diagonals ratio = φ = (1+√5)/2 ≈ 1.618; face angles: arctan(2) ≈ 63.435° and 180° − 63.435° = 116.565°. Rhombic dodecahedron (RD) is the Voronoi cell of face-centered cubic (FCC) lattice — its 12 faces are congruent rhombi with diagonal ratio √2 : 1 (not golden). Golden RD would have diagonal ratio φ : 1, making it a *different* zonohedron — a golden isozonohedron. Icosidodecahedron has 30 vertices, 20 triangles, 12 pentagons; its radial expansion generates RD-like lattices. Double cube construction: RD volume = 2 × cube volume; edge length of RD = √3/2 × cube edge. CONNECTION: Golden ratio φ appears in the *face shape* of golden isozonohedra, but the standard RD (FCC Voronoi) uses √2, not φ. However, the icosidodecahedron itself contains φ in its geometry (pentagons, gold Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Authors
- Andrew Stewart Caldin
Publication Details
- Journal
- Zenodo (CERN European Organization for Nuclear Research)
- Published
- 2026-10-05
- DOI
- https://doi.org/10.5281/zenodo.23152130
- Primary Topic
- Advanced Mathematical Theories and Applications
- Type
- preprint