  The construction of stationary axisymmetric multiwormhole solutions to
gravitating field theories admitting toroidal reductions to three-dimensional
gravitating sigma models is reviewed. We show that, as in the multi-black hole
case, strut singularities always appear in this construction, except for very
special configurations with an odd number of centers. We also review the
analytical continuation of the multicenter solution across the $n$ cuts
associated with the wormhole mouths. The resulting Riemann manifold has $2^n$
sheets interconnected by $2^{n-1}n$ wormholes. We find that the maximally
extended multicenter solution can never be asymptotically locally flat in all
the Riemann sheets.
