Symmetry precludes the use of regular pentagons to tile a surface. However, as the accompanying figure shows, you can tile with irregular pentagons in a pattern known as Cairo tiling, named after the paving on several streets in Egypt's capital. According to a new theoretical study by Qian Wang of Peking University and her collaborators, the same pattern can be realized on the atomic scale: in graphene-like sheets of carbon. Carbon structures that feature pentagons have already been synthesized. The archetypal fullerene, C60, comprises 12 pentagons amid 20 hexagons; the smallest, C20, comprises 12 pentagons. Despite those antecedents, the idea that carbon could be coaxed into forming pentagonal sheets arose not from fullerenes but from a new crystalline phase that was predicted three years ago. Known as T12, the phase has two repeating layers, one of which consists of a corrugated arrangement of Cairo-tiled pentagons. Working on the assumption that the buckled layer could be chemically exfoliated, Wang and her collaborators calculated its properties. Although the material, dubbed penta-graphene, turned out to be metastable, it withstands heating up to 1000 K. It is stronger and somewhat less stiff than graphene, and it can be rolled up to form nanotubes. Unusually, penta-graphene has a negative Poisson's ratio: If you stretch it longitudinally, it will also stretch laterally. And unlike pure graphene, pure penta-graphene is a semiconductor, whose nearly direct 3.25-eV bandgap might make it optically useful. (S. Zhang et al., Proc. Natl. Acad. Sci. USA, in press, doi:10.1073/pnas.1416591112.)
