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We present a single-phase super lens with a low density that can accomplish focusing of sound beyond the difraction limit. The super lens features a star-shaped lattice structure built of steel those offers numerous resonances to generate anomalous dispersive efects as assessed by negative parameter indices. Our research of the metamaterial band structure reveals that these star-shaped metamaterials exhibit double-negative index features that can mediate these efects for sound in water. Simulations verify the efective focusing of sound by a single-phase solid lens with a spatial resolution of roughly 0.39 λ. This superlens has a basic structure, low density and solid nature, which makes it more viable for application in water-based situations. It should be mentioned that the suggested approach may produce a more simple stiffness and mass matrices of the proposed structures, compared with the classic finite element (FE) method. Thereafter, the impacts of the geometrical parameters on the effective constants and band gaps are explored and addressed. Numerical results reveal that the negative Poisson’s ratio produces an improved effective Young’s modulus of the investigated honeycombs. Furthermore, the band gap occurs at a much lower frequency zone with an unaltered summing band gap width when the Poisson’s ratio is in negative values. In general, the work can serve as a guide for the best design of cellular structures.