Editing Shape of the universe (section)

==== Universe with positive curvature ====
A positively curved universe is described by [[elliptic geometry]], and can be thought of as a three-dimensional [[hypersphere]], or some other [[spherical 3-manifold]] (such as the [[Poincaré dodecahedral space]]), all of which are [[Quotient space (topology)|quotient]]s of the 3-sphere.

[[Homology sphere#Cosmology|Poincaré dodecahedral space]] is a positively curved space, colloquially described as "soccerball-shaped", as it is the [[Quotient space (topology)|quotient]] of the 3-sphere by the [[binary icosahedral group]], which is very close to [[icosahedral symmetry]], the symmetry of a soccer ball. This was proposed by [[Jean-Pierre Luminet]] and colleagues in 2003<ref name="Nat03">{{Cite journal |last1=Luminet |first1=Jean-Pierre |author-link1=Jean-Pierre Luminet |last2=Weeks |first2=Jeffrey R. |last3=Riazuelo |first3=Alain |last4=Lehoucq |first4=Roland |last5=Uzan |first5=Jean-Philippe |date=October 2003 |title=Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background |journal=[[Nature (journal)|Nature]] |volume=425 |issue=6958 |pages=593–595 |arxiv=astro-ph/0310253 |bibcode=2003Natur.425..593L |doi=10.1038/nature01944 |issn=0028-0836 |pmid=14534579 |s2cid=4380713}}</ref><ref name="physwebLum03">{{Cite web |last=Dumé |first=Isabelle |date=8 October 2003 |title=Is the universe a dodecahedron? |url=https://physicsworld.com/a/is-the-universe-a-dodecahedron/ |website=[[Physics World]] |language=en-GB}}</ref> and an optimal orientation on the sky for the model was estimated in 2008.<ref name="RBSG08">{{Cite journal |last1=Lew |first1=B. |last2=Roukema |first2=B. |last3=Szaniewska |first3=Agnieszka |last4=Gaudin |first4=Nicolas E. |date=May 2008 |title=A test of the Poincaré dodecahedral space topology hypothesis with the WMAP CMB data |journal=[[Astronomy & Astrophysics]] |volume=482 |issue=3 |pages=747–753 |arxiv=0801.0006 |bibcode=2008A&A...482..747L |doi=10.1051/0004-6361:20078777 |issn=0004-6361 |s2cid=1616362}}</ref>