Group actions are usually far from being determined by their isotropy groups, an exception being the case where the quotient is one dimensional. We give a recipe for constructing new manifolds from potential isotropy groups for so called polar actions. They are defined as a group action for which a submanifold exists intersecting all orbits orthogonally. For example all toric Hamiltonian actions are polar. We give many other examples often defining manifolds that are not easily identifiable as "known" spaces.