The Icosahedral Structure of Twin Primes

We demonstrate that twin primes arise from icosahedral geometry. The prime wheel modulus 66 = D! × (V−1) = 6 × 11 encodes the icosahedron: V = 12 vertices (the kissing number k(3)), F = 20 faces = φ(66) wheel slots, D = 3 dimensions (uniquely selected by D(D+1) = 2×D!). The number of twin prime channels is exactly V − D = 9, a direct consequence of the +2 shift on residues mod 11. The factor D = 3 in the wheel protects twin slots from composite pairs. The 20 slots partition 10/10 into quadratic residues and nonresidues, with the Gauss sum g = i√11 encoding this duality. Twin primes exist because the icosahedral structure creates protected channels.