Icosahedron Vertices Defined by Three Orthogonal Golden Rectangles — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Icosahedron vertex coordinates derive from three mutually perpendicular golden rectangles, linking Platonic solid to golden ratio directly. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.618. Icosahedron vertices: (±1, ±φ, 0), (0, ±1, ±φ), (±φ, 0, ±1). Three golden rectangles (aspect ratio 1:φ) placed orthogonally define all 12 vertices. Symmetry group order = 120 (full icosahedral group, including rotations and reflections). | CONNECTION: φ appears as fundamental constant in vertex coordinates; golden rectangle construction yields φ² = φ+1 = 2.618; reciprocal 1/φ = φ-1 = 0.618; related to pentagonal symmetry (72° angles). Group order 120 = 5! = 5×4×3×2×1, linking to pentagonal and dodecahedral symmetries. | DEPTH: 9 — This is a foundational geometric fact that embeds the golden ratio into the structure of a Platonic solid, revealing deep connections between irrational constants, symmetry groups, and three-dimensional space. The construction is elegant and exact, not approximate. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7170080347
Cites:
Cited by:
Related to: