Unique new ladder polymers consisting of condensed succession of six- and five-membered conjugated carbon rings have been made recently by Scherf and Mullen. This paper compares the electronic structures of six topological isomers of these poly(indenoindenes). The results are analyzed in terms of topological band gaps and geometry relaxation. While all isomers have seven electrons in their chemical repeat units, only a few are expected to have a band gap smaller than 0.5 eV. The possibility of a ferrimagnetic ground state for some low-band-gap isomers is also discussed. Optical properties of the precursor planarized polyphenylenes are analyzed. Present calculations also predict that the transition to the highly conducting state should occur at significantly lower dopant concentrations compared to single-chain conducting polymers, such as polyacetylene or polythiophene.