writes "In the 1970 World Cup in Mexico, teams used a new kind of ball called the Telstar made from 12 black pentagonal panels and 20 white hexagonal panels. This ball has icosahedral symmetry and its own molecular analogue in the form of C60, the famous soccer ball-shaped fullerene. In 2006, a new ball called the TeamGeist was introduced at the World Cup in Germany. This was made of 14 curved panels that together gave it tetrahedral symmetry. This also had a molecular analogue with tetrahedral symmetry among the fullerenes. Now teams at the current World Cup in Brazil are playing with yet another design: the Brazuca, a ball constructed from six panels each with a four-leaf clover shape that knit together like a jigsaw to form a sphere. This has octahedral symmetry. But here's question that has been puzzling chemists, topologists and..errr...soccer fans: is there a molecular analogue of the Brazuca? Or put another way, can fullerenes have octahedral symmetry? Now a pair of mathematicians have finally solved this problem. They've shown that fullerenes can indeed have octahedral symmetry just like the Brazuca, although in addition to hexagonal and pentagonal carbon rings, the ball-shaped molecules must also have rings of 4 and 8 carbon atoms. The next stage is to actually synthesis one of these fullerenes, perhaps something to keep chemists occupied until the 2018 World Cup in Russia."