Penrose Star 1

The Penrose tiling is an aperiodic tiling made of two shapes - a kite and a dart. While periodic tilings like a checkerboard or a tessellation of hexagons and triangles always repeat in a regular pattern, there is no overall periodic repetition throughout the Penrose tiling. That is, each small section of the Penrose tiling (like this star) will appear infinitely many times in the tiling, but these small sections are put together according to a rule to ensure they don't form a bigger pattern. 

The kite and dart tiling in this pattern is officially the 'P2' Penrose tiling. There are others: 'P1' made of a star, a 'boat', and a rhombus, and 'P3' made of two sizes of rhombus. These tilings are named after Sir Roger Penrose, who discovered them in the 1970s.