Periodic skyrme solitons

We discuss the possibility of new topological structures in the context of the Skyrme model. It is argued that periodic boundary conditions on the chiral field yield mappings from nonspherical group manifolds onto S3. A one-parameter family of maps from S2×S1 onto S3 is explicitly constructed, and shown to reproduce linear, periodic, baryonic forms with an even clustering of baryons. Explicit numerical solutions are obtained, and their relevance to hadronic matter is discussed.