It has been my understanding from various articles I've been reading by Jeff Weeks and others that there was a strong belief that the shape of the Universe was the Poincare Dodecahedral Space (PDS), based upon the WMAP data's missing certain larger frequencies and the given range for the curvature from the 3-year WMAP to be 1.02 +/- 0.02. That range went from 1.00 to 1.04 in the 3 year WMAP data to approximately 0.9934 to 1.0178 in the 5-year WMAP data (using the LAMBDA version). I read that the shape of the Universe being the shape of the PDS rested largely on Omega being close to 1.02, which was well within the previous range for the density/curvature of the universe. Now that the range has altered, it seems that the PDS is not as likely to be the shape of the Universe, at least it is outside of the 95% confidence interval. Has anyone heard of any other proposed 3D models that would replace the PDS? I'm currently reading through Topological Lensing on Spherical Spaces by Gausmann, Luminet, Weeks and others which is a paper that classifies positively curved 3D spaces. You can find the paper at the link: http://arxiv.org/PS_cache/gr-qc/pdf/0106/0106033v1.pdf However the paper was written well before the most recent data from the WMAP was released and I doubt I will be able to use it to determine the new model, so if you can point me in a better direction with a different paper that would be appreciated as well.