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Following a solution generating technique introduced recently by one of us,we transform the Einstein static Universe into a two - fold infinity class ofphysically acceptable exact perfect fluid solutions of Einstein's equations.Whereas the entire class of solutions can be considered as generalizations ofthe familiar Tolman IV solution, no member of the class can be writtenexplicitly in isotropic coordinates. Further, except for a set of measure zero,no member of the class can be written explicitly in curvature coordinateseither.

Transforming the Einstein static Universe into physically acceptable static fluid spheres II: A two - fold infinity of exact solutions