  We construct solutions of plane symmetric wormholes in the presence of a
negative cosmological constant by matching an interior spacetime to the
exterior anti-de Sitter vacuum solution. The spatial topology of this plane
symmetric wormhole can be planar, cylindrical and toroidal. As usual the null
energy condition is necessarily violated at the throat. At the junction
surface, the surface stresses are determined. By expressing the tangential
surface pressure as a function of several parameters, namely, that of the
matching radius, the radial derivative of the redshift function and of the
surface energy density, the sign of the tangential surface pressure is
analyzed. We then study four specific equations of state at the junction: zero
surface energy density, constant redshift function, domain wall equation of
state, and traceless surface stress-energy tensor. The equation governing the
behavior of the radial pressure, in terms of the surface stresses and the
extrinsic curvatures, is also displayed. Finally, we construct a model of a
plane symmetric traversable wormhole which minimizes the usage of the exotic
matter at the throat, i.e., the null energy condition is made arbitrarily small
at the wormhole throat, while the surface stresses on the junction surface
satisfy the weak energy condition, and consequently the null energy condition.
The construction of these wormholes does not alter the topology of the
background spacetime (i.e., spacetime is not multiply-connected), so that these
solutions can instead be considered domain walls. Thus, in general, these
wormhole solutions do not allow time travel.
