  It is generally agreed that the acceleration of the Universe can best be
explained by the presence of dark or phantom energy. The equation of state of
the latter shows that the null energy condition is violated. Such a violation
is the primary ingredient for sustaining traversable wormholes. This paper
discusses wormholes supported by a more general form called polytropic phantom
energy. The equation of state results in significant generalizations of the
phantom-energy and, in some cases, the generalized Chaplygin-gas wormhole
models, both of which continue to receive considerable attention from
researchers. Several specific solutions are explored, namely, a constant
redshift function, a particular choice of the shape function, and an
isotropic-pressure model with various shape functions. Some of the wormhole
spacetimes are asymptotically flat, but most are not.
