We present a rigorous resolution to the Nielsen-Ninomiya “No-Go” theorem by deriv- ing fermion chirality from the non-bipartite topology of a saturated cuboctahedral vacuum (K = 12). Standard hypercubic discretizations of the Dirac equation inevitably produce spurious mirror fermions due to the bipartite symmetry of the grid. We demonstrate that a Face-Centered Cubic (FCC) lattice, formed of simplicial tetrahedra, introduces topological frustration that breaks this symmetry. By explicitly constructing the discrete Dirac operator and specifying the Γj matrices as spin projections along the 12 bond directions, we evaluate the dispersion relation across the first Brillouin zone. We show that while the physical mode at the Γ-point is massless, doubler modes at the L and X points are lifted to the Planck cutoff. To validate this geometric framework, we derive the bare Higgs coupling λ ≈0.125 from the ratio of surface-to-volume configurations, predicting a mass of 123.11 GeV. Keywords: Fermion Doubling, Nielsen-Ninomiya Theorem, Lattice Field Theory, Higgs Mass, Grav- itational Echoes, Selection-Stitch Model