We study compact U (1) lattice gauge theory on the face-centred cubic (FCC) lattice with geometric coupling g² = π²/108, extending the framework of Paper I. The octahedral symmetry group Oₕ decomposes the 12 gauge link degrees of freedom into five irreducible representations. A parity selection rule, exact by Schur's lemma, renders all gerade channels massless while ungerade channels acquire mass. The T₁u channel, identified as the charged-particle channel by its vector coupling, is the heaviest mode. The Polyakov monopole-instanton mechanism with exact Hessian eigenvalues, computed on lattices of size N = 6 through N = 14, yields a fermion mass of 0. 508 ± 0. 010 MeV after chiral correction; the experimental electron mass (0. 511 MeV) lies within one standard deviation. The mass formula is validated against published Monte Carlo measurements on the cubic lattice. We prove that FCC is the unique Bravais lattice whose nearest-neighbour coordination (z = 12) permits the 8+3+1 irreducible-representation partition consistent with the Standard Model gauge structure, and show that all five major experimental Lorentz violation constraints are satisfied. Erratum (12 April 2026): Section 8. 2 corrected. The staggered fermion count of 24, 264 is erroneous (bipartite test incorrectly applied to FCC's 4-sublattice structure). The correct count is 24 = |O| (chiral octahedral group). The 95 naive doublers decompose as 95 = 2|Oₕ| - 1 = 48 + 47. See Paper IV for details.
Andrew Wright (Sun,) studied this question.