The Penrose P3 tiling uses two rhombs (fat and thin, golden ratio proportions) to tile the plane aperiodically — it never repeats, yet has 5-fold rotational symmetry. Generated by deflation.
Penrose tiling has no translational symmetry — it is aperiodic — yet long-range order. The ratio of fat to thin rhombs → golden ratio φ ≈ 1.618. Quasicrystals (Nobel Physics 2011) exhibit exactly this structure in 3D.
← Back to Lab