Interpenetrating Networks of Three-Dimensional Penrose Tiles in CaAu₃Ga, the Structurally Simplest Cubic Approximant of an Icosahedral Quasicrystal

Double-Friauf polyhedra (DFPs) which play important roles in quasicrystal (QC) models are the unique building blocks in the novel 1/0 AC, CaAu3+ΔGa1−Δ (Δ ≈ 0–0.13) [Pa3̅; a = 9.0875(3)–9.1107(5) Å]. The packing of DFPs generates interpenetrating networks of condensed three-dimensional Penrose tiles, the geometry of which is close to that assumed for QCs.