Roger Penroseborn 1931
Aperiodic tiling system
British mathematical physicist whose non-periodic tilings and work on impossible geometry reshaped how repetition and symmetry are understood.
Penrose Tiles
Kites and darts that cover the plane without ever repeating. Five-fold symmetry, golden-ratio edges, and no translational grid.
About this pattern
Roger Penrose, 1974
Start with a sun of ten Robinson triangles and deflate. Thin and thick triangles become kites and darts; edges of length φ never line up into a repeating lattice. Five-fold symmetry is allowed here, unlike a crystal.
Behind the mathematics