In this work, we define quasicrystalline spin networks as a subspace within the standard Hilbert space of loop quantum gravity, effectively constraining the states to coherent states that align with quasicrystal geometry structures. We introduce quasicrystalline spin foam amplitudes, a variation of the Engle–Pereira–Rovelli–Livine (EPRL) spin foam model, in which the internal spin labels are constrained to correspond to the boundary data of quasicrystalline spin networks. Within this framework, the quasicrystalline spin foam amplitudes encode the dynamics of quantum geometries that exhibit aperiodic structures. This study serves as the first step toward understanding how these structures can contribute to the semiclassical limit of quantum gravity models, with potential future applications to cosmology. The interest in such applications has been revitalized due to the Hubble tension, which motivates further exploration of quantum effects in large-scale cosmological scenarios. Additionally, we investigate the coupling of fermions within the quasicrystalline spin foam amplitudes. We present calculations for three-dimensional examples and then explore the 600-cell construction, which is a fundamental component of the four-dimensional Elser–Sloane quasicrystal derived from the E8 root lattice.