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The problem of the design of artificial magnetic resonators for isotropic metamaterials is addressed. The internal symmetries that ensure an isotropic behavior of such resonators are analyzed and some specific designs based on the proper arrangement of modified split ring resonators are proposed. These proposals are validated by electromagnetic simulations and experiments. The reported results are likely to have applications in the design of devices such as negative refractive index materials, superlenses, and metasurfaces with isotropic response.