  We consider a topologically nontrivial thin-shell wormhole with a throat in
the form of a $T^2$ torus. It is shown that: (i)~such a wormhole is stable with
respect to excitations of the throat; (ii)~not all energy conditions are
violated for such wormholes; (iii)~if any of the energy conditions is violated,
this violation occurs only partially in some region near the throat, and in
other regions the violation is absent. Also, we discuss the differences between
spherical $S^2$ wormholes and toroidal $T^2$ wormholes under investigation.
