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THERE are five Platonic solids of perfect symmetry. Three, the tetrahedron, octahedron and icosahedron, have triangular faces. A fourth, the cube, has square faces. The fifth, the dodecahedron, has pentagonal faces. Plato believed that the first four corresponded to the elements of which the Greeks thought the material world was composed: fire, air, water and earth. The dodecahedron, however, corresponded to quintessence, the element of the heavens. As Plato put it, “God used this solid for the whole universe, embroidering figures on it.” And if the arguments of a paper in this week's Nature stand up, Plato will have been proved right. For Jean-Pierre Luminet, of the Paris Observatory, and his colleagues believe that the universe is, indeed, a dodecahedron.

The myth-makers Jan 3rd 2002 Space Mr Luminet and colleagues' article is published in Nature.

They base their argument on data collected by the Wilkinson Microwave Anisotropy Probe (WMAP). This American satellite has been examining the microwave radiation generated shortly after the universe began. The wavelength of this radiation is remarkably pure, but like a musical note it has harmonics associated with it. These harmonics, like those of a note, reflect the shape of the object in which the waves were generated. In the case of the note, that object is a musical instrument. In the case of the microwave background, that object is the universe itself.

The most widely accepted model of the universe suggests that it is both flat and infinite. In this case, flatness does not mean it is two-dimensional, but that the space of which it is composed has no large-scale curves in it. (Small curves induced by gravitational fields, and predicted by the theory of relativity, do exist.) WMAP's data are in close agreement with this model, but that agreement is not perfect. In particular, the second and third harmonics of the microwave radiation are weaker than expected. Dr Luminet's calculations suggest that this weakness can be explained if the universe is finite and dodecahedron-shaped. Of course, things are not quite that simple. Familiar dodecahedrons have an inside and an outside. What Dr Luminet is proposing is actually something called a dodecahedral space, first described by his countryman Jules-Henri Poincaré in the 19th century. Such a space has no boundary, even though it has a finite volume. But it is, quintessentially, a dodecahedron. One up to the Greeks.