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We propose a new topology for realizing artificial microwave materials that exhibit a negative refractive index over a wide frequency band. These metamaterials consist of a three-dimensional transmission line mesh that is loaded with reactive series and shunt elements to create negative permittivity and permeability. The cubic-cell transmission line host network is a physical realization of the 3D distributed node TLM lattice which has the same low-frequency properties as the FDTD Yee scheme. This paper describes the topology, the theory, the design, and possible realizations of such a metamaterial. Its wave properties are validated by full-wave simulations using the time domain electromagnetic field simulation tool MEFiSTo-3D Pro.