It is known that including vector mesons stabilizes the size of a Skyrmion without the need for a Skyrme term. This paper provides the first results for static multi-Skyrmions in such a theory. The rational map ansatz is used to investigate multi-Skyrmions in a theory which includes the omega vector meson and has no Skyrme term. Bound states with baryon numbers two, three and four are found, which have axial, tetrahedral and cubic symmetries, respectively. The results reveal a qualitative similarity with the standard Skyrme model with a Skyrme term and no vector mesons, suggesting that some features are universal and do not depend on the details of the theory. Setting the pion decay constant and meson masses to their experimental values leaves only a single free parameter in the model. Fixing this parameter, by equating the energy of the baryon number four Skyrmion to the Helium-4 mass, yields reasonable results for other baryon numbers.

Version to appear in Phys. Rev. D