However, examination of medieval Islamic decorations, called girih patterns, reveal plenty of five and ten-fold symmetric patterns that, apparently, do tile a surface.

We demonstrated three patterns without translational symmetry. These include a star shape, a five-fold Penrose tiling and an eight-fold quasi-crystalline pattern (Fig. 3a–c).

The illustration showed a curious tiling of black and white triangles with curved sides. Enclosed within a circle, the alternately colored triangles became progressively smaller as they approached ...

The tiling stood as a unique mathematical breakthrough – until 2005, when Harvard graduate student Peter Lu discovered variations of the same non-periodic tiling patterns on a 17th-century ...

It’s easy to tile triangles and quadrangles because we’ve all seen graph paper, or been stuck on a boring phone call with a pen and notepad handy. It’s a little trickier to envision tiling ...

Thus, all triangles and quadrilaterals—even irregular ones—admit an edge-to-edge monohedral tiling of the plane. But with irregular pentagons, things aren’t so simple.

New research sheds light on how a certain kind of pattern in nature arises. Nature is full of patterns. Among them are tiling patterns, which mimic what you'd see on a tiled bathroom floor ...