The intriguing bis!(1,2,3,4-trithiazolium) dication (CNS3)(2)(2+) is a triplet state system, even in the solid state. Prompted by this molecule, we propose and theoretically study several hypothetical polymers, in the hope that they will display magnetic ordering. We seek systems in which the valence band is half-filled and as narrow as possible. In order to achieve that, We use as monomer units the members of a fascinating family of seven-pi;-electron, five-membered heterocycles which are closely related to (CNS3)(2)(2+). In these compounds, the highest two pi orbitals are "distinct" from all the other orbitals. The uniqueness of these orbitals carries over in a systematic way into the extended systems (ortho-or meta-linked) which they form. Because the monomers have seven pi electrons, the polymers have half-filled valence bands. We try to exploit the differences among the many possible heterocycles to provide polymers with narrow valence bands. Three such polymers, poly(cyclo-CSSSC+), poly(cyclo-CSSNC), and poly(cyclo-CSNSN+), are found to have valence bands approximately 0.3 eV wide; the first two are helical, and the third is planar.