Penrose Matching Rules from Realistic Potentials in a Model System

We exhibit a toy model of a binary decagonal Al-Co quasicrystal – closely related to actual structures – in which realistic pair potentials yield a ground state which appears to perfectly implement Penrose’s matching rules, for Hexagon-Boat-Star (HBS) tiles of edge 2.45 A. The second minimum of the potentials is crucial for this result.