Recently, Lagos et al [Nat. Nanotechnol. 4, 149 (2009)] reported the discovery of the smallest possible silver square cross-section nanotube. A natural question is whether similar carbon nanotubes can exist. In this work we report ab initio results for the structural, stability, and electronic properties for such hypothetical structures. Our results show that stable (or at least metastable) structures are possible with metallic properties. They also show that these structures can be obtained by a direct interconversion from SWNT(2,2). Large finite cubanelike oligomers, topologically related to these new tubes, were also investigated.
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