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

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
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preprint

Golden Isozonohedra from Icosidodecahedra: A Geometric Link to FCC Lattice — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
preprint

Golden Isozonohedra from Icosidodecahedra: A Geometric Link to FCC Lattice — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

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

Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Theories and Applications
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Golden Isozonohedra from Icosidodecahedra: A Geometric Link to FCC Lattice — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS