A recently proposed system with a central planar tetracoordinate carbon linking two three-membered rings, C-5(2-), lends itself to extension in one, two, and three dimensions. Our construction of potential realizations begins with an analysis of the electronic structure of C-5(2-). Dimers such as C10Li3-, C10Li4, and a trimer C15Li6 are then examined, and their geometries are optimized to find clues for ways the C-5(2-) unit may polymerize in the presence of countercations. Coordination through the terminal carbons is favored in the oligomers and polymers; several electronically and structurally reasonable systems of the stoichiometry C5Mx (M = Li, x = 2; M = Be, Pt, Zn, x = 1) emerge from band structure calculations and energetic considerations.