The face-centered cubic (FCC) lattice has two classes of interstitial voids: tetrahedral voids with coordination 4, and octahedral voids with coordination 6. A trapped extra node at either type of void can be treated as a localized point defect coupled to the surrounding FCC sites through nearest-neighbor bonds. This paper computes the bound-mode multiplet of the naive Dirac operator at each defect class and decomposes it under the residual point-group symmetry. At a tetrahedral defect, the bound multiplet has dimension 4 and decomposes under Td, isomorphic to S4, as A1 + T2. In the Schoenflies Td convention used in the paper, the three-dimensional T2 representation is the polar-vector representation. At an octahedral defect, the bound multiplet has dimension 6 and decomposes under Oh as A1g + Eg + T1u. Both three-dimensional pieces are spatial-vector representations, so the spectral labels alone do not distinguish the two defect classes. The decisive distinction is combinatorial. For the tetrahedral defect, the three-dimensional T2 piece has the same dimension as, and is S3-module-isomorphic to, the internal color space built in Kulkarni’s companion matter paper from the three perfect matchings of K4, the bonded graph of the tetrahedral defect’s surrounding sites. For the octahedral defect, the bonded graph of the six surrounding sites is K2,2,2 rather than K6, because the three antipodal vertex pairs sit at second-nearest-neighbor distance in the FCC lattice and are not physical bonds. This K2,2,2 graph has 8 perfect matchings and 30 skew-edge pairs, neither of which gives the same three-color structure. The spectral analysis is therefore a dimensional consistency check on a prior combinatorial color assignment, not a derivation of color from the spectrum. The tetrahedral bound triplet has the dimension of the K4 color space, while the two defect classes are separated by their matching structure rather than by the existence of a spatial-vector triplet alone. A companion dark-matter paper reaches the same K2,2,2 obstruction by independent combinatorial means and proposes a dark-sector identification of the octahedral defect; the present paper supports only the structural distinction underlying that proposal, not its mass scale, abundance, or phenomenology. As supporting background, the paper also classifies the free-field FCC zero-mode spectrum using an exact factorization of the kinetic vector field. The comparison with HCP, BCC, and bulk-modified fermion constructions, and the reasons FCC is selected as an isotropic substrate, are developed in the body of the paper.