In 1982 Dan Shechtman discovered a crystal that would revolutionise chemistry. He has just been awarded the 2011 Nobel Prize in Chemistry for his discovery — but has the Nobel committee missed out a chance to honour a mathematician for his role in this revolution as well?
Squares do it, triangles do it, even hexagons do it — but pentagons don't. They just won't fit together to tile a flat surface. So are there any tilings based on fiveness? Craig Kaplan takes us through the five-fold tiling problem and uncovers some interesting designs in the process.
This pattern with kite-shaped tiles can be extended to cover any area, but however big we make it, the pattern never repeats itself. Alison Boyle investigates aperiodic tilings, which have had unexpected applications in describing new crystal structures.