  We study the stability of different higher dimensional thin--shell wormholes
(HDTSW) in general relativity with a cosmological constant. We show that a
$d$--dimensional thin--shell wormhole surrounded by quintessence can have three
different throat geometries: spherical, planar and hyperbolic. Unlike the
spherical geometry, the planar and hyperbolic geometries allow different
topologies that can be interpreted as higher-dimensional domain walls or branes
connecting two universes. To construct these geometries, we use the
cut-and-paste procedure by joining two identical vacuum spacetime solutions.
Properties such as the null energy condition and geodesics are also studied. A
linear stability analysis around the static solutions is carried out. Our
stability analysis takes into account a more general HDTSW geometry than
previous works so it is possible to recover other well-known stability HDTSW
conditions.
