Unique new ladder polymers consisting of condensed succession of six a
nd five membered conjugated carbon rings have been made recently by Sc
herf and Mullen. Seven topological isomers of these polyindenoindenes
are considered theoretically. The results are analyzed in terms of top
ological bandgaps and geometry relaxation. Three isomers are expected
to have a bandgap smaller than 0.2 eV, although the possibility of a f
errimagnetic ground state for these can not be ruled out.