Whether or not the Golden Ratio or the Golden Rectangle are of aesthetic significance, the ratio does turn out to have considerable significance in problems of natural symmetry. For instance, a surface can be completely and symmetrically tiled with triangles, squares, and hexagons, but not with pentagons. Periodic five-fold symmetry does not occur in nature. However, in the early 70's Roger Penrose discovered that a surface could be completely tiled in an asymetrical and non-periodic way with just two shapes, called "kites" and "darts" -- "Penrose tiles" -- as seen at right. Within this tiling... there can be small areas of five-fold symmetry. Multiple decagons, some of which from a distance can look like pentagons, can occur.