In the 1960s, a Danish company, seeking to improve on the traditional football made from the bladder and stomach of animals, invented the modern football. The designers realised that to form a perfect ball they needed to combine 20 leather hexagons with 12 pentagons, and in so doing demonstrated one of the basic laws of shape – that you cannot wrap a sheet of six-sided hexagons around a sphere. To induce the sheet to bend, the company had to introduce five-sided pentagons alongside the hexagons.
On the micro scale, the human immunodeficiency virus (HIV), which causes AIDS, faces a similar challenge during the assembly of new viral particles: how to coerce its hexagonshaped building blocks to form the spherical envelope that
surrounds its viral innards. Lifting a page from the football manual, structural biologist John Briggs, group leader at EMBL Heidelberg, wondered if HIV likewise solved this shape conundrum by introducing pentagons between the hexagons.
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