  We discuss new exact solutions of a three-parameter nonminimal
Einstein-Maxwell model. The solutions describe static spherically symmetric
objects with and without center, supported by an electric field nonminimally
coupled to gravity. We focus on a unique one-parameter model, which admits an
exact solution for a traversable electrically charged wormhole connecting two
universes, one asymptotically flat the other asymptotically de Sitter ones. The
relation between the asymptotic mass and charge of the wormhole and its throat
radius is analyzed. The wormhole solution found is thus a nonminimal
realization of the idea of Wheeler about charge without charge and shows that,
if the world is somehow nonminimal in the coupling of gravity to
electromagnetism, then wormhole appearance, or perhaps construction, is
possible.
