Most astronomers think that the universe is infinite, but recent measurements suggest that it could be finite and relatively small. Indeed, as Jean-Pierre Luminet describes, we could be living in an exotic universe shaped rather like a football:
Advanced models of cosmology involve the tessellation (tiling) of 3D-hyperspheres by Platonic Solids in a 4-dimensional algebraic setting, the Quaternion algebra or hypercomplex numbers. Of particular interest is the so called Poincaré Dodecahedral Space:
In 2003, lack of structure on the largest scales (above 60 degrees) in the cosmic microwave background as observed for one year by the WMAP spacecraft led to the suggestion, by Jean-Pierre Luminet of the Observatoire de Paris and colleagues, that the shape of the Universe is a Poincaré sphere. In 2008, astronomers found the best orientation on the sky for the model and confirmed some of the predictions of the model, using three years of observations by the WMAP spacecraft. There is as yet no strong support for the correctness of the model, however.