Sonic metamaterials have a wide range of applications in wave control and super-resolution imaging, and are favored for their several unique and advantageous properties. However, current double-negative sonic metamaterials have complex structures composed of various materials, which limits their design and application. Thus, we must produce double-negative features using a simple structure of one material. Because of their unique concave configurations and various resonances, star-shaped structures readily form band gaps and show superior material properties. In this study, we designed and simulated star-shaped single-phase metamaterials, considered ideal structures. Our numerical results suggest that these metamaterials have two band gaps as well as double-negative properties over specific frequency ranges. Moreover, we investigated how their band gap and double-negative properties depended on the concave angle.