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At very low frequencies, the electric field integral equation discretization requires the extraction of the solenoidal part of the current to circumvent problems resulting from the severe poor conditioning of the method of moments matrix. Here we describe how the solenoidal or loop bases can be generated on bodies composed of arbitrarily shaped surfaces connected to wires. Moreover we present an automatic, low-complexity algorithm to extract the closed paths from the underlying mesh for complex wire-surface structures, either free-standing or connected to an infinite ground plane. The performance of the proposed basis is confirmed by the reported numerical examples.