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