Here's a look at the shape that can tile the plane in a non-repetitive pattern — and some of the creative uses people have found for it.

A brand-new pentagon to tile your wall with.

The laws of symmetry are unforgiving, but a team of researchers from the US have come up with a pattern-producing technique that seems to cheat them. The new technique is called moiré nanolithography and the researchers hope that it will find useful applications in the production of solar panels and many other optical devices.

Mathematicians offer new proof of quasicrystals' strange electronic properties.

Will we ever be able to make computers that think and feel? If not, why not? And what has all this got to do with tiles? Plus talks to Sir Roger Penrose about all this and more.

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.