## symmetry

*any*tilings based on fiveness?

**Craig Kaplan**takes us through the five-fold tiling problem and uncovers some interesting designs in the process.

**Winner of the general public category**. Enormous is the right word: this theorem's proof spans over 10,000 pages in 500 journal articles and no-one today understands all its details. So what does the theorem say?

**Richard Elwes**has a short and sweet introduction.

**Mario Livio**explains how not only shapes, but also laws of nature can be symmetrical, and how this aids our understanding of the universe.

*Plus*finds out about the role of mathematical

**symmetry in chemistry**.