We construct regular multi-wormhole solutions to a gravitating $σ$ model in three space-time dimensions, and extend these solutions to cylindrical traversable wormholes in four and five dimensions. We then discuss the possibility of identifying wormhole mouths in pairs to give rise to Wheeler wormholes. Such an identification is consistent with the original field equations only in the absence of the $σ$-model source, but with possible naked cosmic string sources. The resulting Wheeler wormhole space-times are flat outside the sources and may be asymptotically Minkowskian.

17 pages, LaTeX, 4 figures (hard copy available on request)