How can the universe be dodecahedron-shaped? Physicsworld references "Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background" by J.-P. Luminet et al., published in Nature (Nature 425 (2003) 593).
They claim that a universe with the same shape as the twelve-sided polygon can explain measurements of the cosmic microwave background.
How could this be true? I thought the universe's shape is spherically symmetric. Does this mean the universe has sharp edges (like a dodecahedron)?! Doesn't this mean that the universe prefers some directions to the others?
 A: The universe is not believed to have a boundary. But the global topology of space does not have to be a 3-sphere $S^3$ (for constant positive curvature), infinite flat space $R^3$ (for zero curvature) or a 3D hyperbolic pseudosphere $H^3$ (for negative curvature). General relativity only describes the local structure and curvature, not the global topology. 
The Killing–Hopf theorem (all complete connected Riemannian manifolds of constant curvature are isometric to a quotient of a sphere, Euclidean space, or hyperbolic space by a group acting freely and properly discontinuously) indicates that for constant curvature spaces various topologies are possible. These correspond to taking a chunk of one of the "default" spaces mentioned above and identifying the faces so that going through one of them means one enters the volume from one of the other faces. The most obvious is taking a box of flat space and identifying opposite faces so it acts as a 3-torus.
It is possible to construct several nontrivial finite volume zero or positively curved spaces (and even more for negative curvature, where there might be an infinite number of possibilities).  The Poincaré Dodecahedral Space, formed by identifying opposite faces of a regular dodecahedron after a 36 degree rotation, has been discussed as a cosmological model. This is the one the question dealt with. The reason for the shape is that it corresponds to a particular symmetry group of the sphere, the extended icosahedron group. While the space can be defined in many ways, they are all equivalent (and different from the spaces when one uses a different group).
This kind of space is in one sense spherically symmetric: the curvature is constant. But all directions are not the same, so it is not quite isotropic. There are no sharp edges, since the joining up is smooth (even in the "corners"). Most importantly, it would act as a "hall of mirrors" where distant objects would be repeated in some pattern if their light has reached us. This allows for searching for the topology by looking at correlations in the cosmic microwave background along circles on the sky (their sizes are set by the size of the space and its topology).
There is currently no evidence for a nontrivial topology. WMAP placed a limit of 25.6  giga parsec on the cell size, even for very general topologies. The Planck collaboration placed limits on the radius $R_i$ of the largest inscribed sphere in the topological domain compared to the co-moving distance to the last surface of scattering $\chi\approx 14.0$ Gpc. They found that for a flat universe, $R_i>0.92\chi$ for the 3-torus, $R_i>0.71$ for the prism, and $R_i>0.5\chi$ for the slab, while in a positively curved universe $R_i>1.03\chi$ for the dodecahedral space, $R_i>1.0\chi$ for the truncated cube, and $R_i>0.89\chi$ for the octahedral space. For other considered topologies $R_i>0.94\chi$ at the 99% confidence level.
A: If you read the abstract of the article given in the comments you will see that there does exist an not explainable with a spherical model angular distribution:

Temperature correlations across the microwave sky match expectations on scales narrower than 60∘, yet vanish on scales wider than 60∘.  

It is this anisotropy modeled with a dodecahedron. After all crystals exist in nature, no? of all types . There are no sharp corners, but angular distributions in the xrays of crystals that define the faces of the geometrical model needed.
Something analogous is postulated to explain the observations. 
