Penrose tilings, cluster models and the quasi-unit cell picture

The quasi-unit cell picture proposes that quasicrystals can be decomposed into a single, repeating cluster of atoms with overlap (atom-sharing) rules between neighbors that force a perfect quasiperiodic structure. In this paper, we introduce the basic features of the model and how it differs from the earlier Penrose tiling and cluster models. We also report on recent advancements in applying the model to determine the structure of the decagonal phase, Al₇₂Ni₂₀Co₈, including new evidence supporting the quasi-unit cell picture based on clusters with broken 10-fold symmetry in favor of models based on unbroken symmetry.