Golden Rectangles Construct the Icosahedron — E8 Intelligence Research
Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) · 2026
FINDING: The icosahedron is constructible from three mutually perpendicular golden rectangles; its vertices are the 12 corners of these rectangles, yielding exact edge-length and circumradius/inradius ratios in terms of φ. | MATH: Let φ = (1+√5)/2 ≈ 1.6180339887. Place three golden rectangles with aspect ratio φ:1, centered at origin, each in a coordinate plane (xy, xz, yz), with long sides along two axes and short sides along the third. Their 12 corners have coordinates (±φ, ±1, 0), (±φ, 0, ±1), (0, ±φ, ±1) — all permutations with one zero and two nonzero entries (φ and 1). Edge length s = 2 (distance between (φ,1,0) and (φ,−1,0) is 2; adjacent vertices like (φ,1,0) and (1,φ,0) have distance √[(φ−1)² + (1−φ)²] = √[2(φ−1)²] = √[2(1/φ²)·2]? — check: φ−1 = 1/φ, so distance = √[2·(1/φ)²] = √2/φ ≈ 0.874 — wait, that's not 2. Correct: adjacent vertices are (φ,1,0) and (φ,0,1): distance = √[0² + 1² + 1²] = √2. But edge length of icosahedron from this construction is actually 2 (the short sid Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com