Is the universe a dodecahedron?
Plato assigned the dodecahedron to the whole. In 2003 cosmologists proposed that space itself might have the shape of a dodecahedron, based on the cosmic background radiation.
In the Timaeus Plato assigns four of the five regular solids to the elements: the tetrahedron to fire, the octahedron to air, the icosahedron to water and the cube to earth. The fifth, the dodecahedron of twelve pentagons, is left over. This one, Plato writes, the god used for the whole, to embroider it with figures (see The Platonic solids). The dodecahedron as the shape of the universe: it sounds like pure mythology.
The dodecahedron, twelve regular pentagons. For Plato the shape of the whole.
A finite space without an edge
Almost two and a half thousand years later the idea resurfaced in cosmology. Relativity says how space is curved, but not what overall shape it has. It could be infinite, or finite and yet without an edge, just as the surface of a sphere is finite and nevertheless never ends.
One of the strangest of these possible shapes is the Poincaré dodecahedral space, described by the mathematician Henri Poincaré in 1904. Imagine a dodecahedron whose opposite faces are joined, each twisted against the other by a tenth of a full turn, 36°. Whoever flies out through one face comes back in through the opposite one. Such a space is finite but has no edge, and from inside one would see oneself in many twisted copies.
The background radiation
In 2003 a team led by the French cosmologist Jean-Pierre Luminet proposed in the journal Nature that the universe might have exactly this shape. The occasion was the measurements of the WMAP space probe. The cosmic background radiation, the oldest light in the universe, showed less variation on the largest angular scales than an infinite space would lead one to expect. A finite dodecahedral space would cut off precisely these large oscillations, just as a small room cannot hold deep notes.
If space were a dodecahedron, one should find pairs of circles with matching patterns in the sky, where the faces of the dodecahedron cut the sphere of the visible universe. The search for them, most recently with the more precise data of the Planck satellite, has not found such circles. Most cosmologists therefore now consider the dodecahedron hypothesis unlikely, though a finite space of this kind is not entirely ruled out if it is large enough.
What remains
Whether the universe really is a dodecahedron remains open, and the data rather speak against it. Something else is remarkable: with the means of modern physics, the question of the shape of the whole has become a serious question again, and among the answers seriously tested was exactly the solid Plato gave to the universe. The dodecahedron is at the same time the figure of five, of the golden ratio and of the pentagram (see The pentagram and the golden ratio).