Universe with positive curvature
Universe with positive curvature Universe in an expanding sphere. The galaxies farthest away are moving fastest and hence experience length contraction and so become smaller to an observer in the centre . 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 quotients of the 3-sphere. Poincaré dodecahedral space , a positively curved space, colloquially described as "soccerball-shaped", as it is the 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 and an optimal orientation on the sky for the model was estimated in 2008.