The Icosahedral Structure of Prime Distribution

We demonstrate that five major prime conjectures — Twin Primes, Goldbach, Legendre, Cramér, and Near-Square Primes — all follow from the same icosahedral geometry that determines D = 3 spatial dimensions. The key insight is that primes are not randomly distributed but are resonance points governed by Wilson's theorem, with the structure 2D² ± 1 generating twin primes at special dimensions. At D = 3 (where D(D+1) = 2×D!), we find 2D² = 18 bracketed by the twin primes 17 and 19. At D = 6 = 2×3, we find 2D² = 72 bracketed by twins 71 and 73. The icosahedron (V=12, E=30, F=20) encodes prime distribution through E − V + 1 = 19, the upper twin at D = 3. Prime density, governed by Wilson resonance and factorial closure (D! = 6), guarantees the required prime existence in each case.