  This paper presents a new wormhole solution by assuming that a homogeneously
distributed fluid with equation of state $p=\omega\rho$ can be adapted to an
anisotropic spacetime such as a wormhole and that this spacetime admits a
one-parameter group of conformal motions. The pressure $p$ in the equation of
state becomes the lateral pressure $p_t$ instead of the radial pressure $p_r$,
as assumed in previous studies. Given that $p_t=\omega\rho$, $p_r$ is then
determined from the Einstein field equations. A wormhole solution can be
obtained only if $\omega <-1$ or $0<\omega <1$. Since the former case
corresponds to phantom dark energy, which has been the subject of earlier
studies, we concentrate mainly on the latter. This case implies that given the
above conditions, dark matter can support traversable wormholes.
