Editing Geometrization conjecture (section)

===Spherical geometry S<sup>3</sup>===
{{Main|Spherical geometry}}
The point stabilizer is O(3, '''R'''), and the group ''G'' is the 6-dimensional Lie group O(4, '''R'''), with 2 components. The corresponding manifolds are exactly the closed 3-manifolds with finite [[fundamental group]]. Examples include the [[3-sphere]], the [[Poincaré homology sphere]], [[Lens space]]s.  This geometry can be modeled as a left invariant metric on the [[Bianchi classification|Bianchi group of type IX]]. Manifolds with this geometry are all compact, orientable, and have the structure of a [[Seifert fiber space]] (often in several ways). The complete list of such manifolds is given in the article on [[spherical 3-manifold]]s. Under Ricci flow, manifolds with this geometry collapse to a point in finite time.