Bis-1,2,4-triazines were explored as potential ground-state triplet molecules which might serve as components of ferromagnetic materials. Relationships between numbers of rings and singlet-triplet gaps were explored by hybrid density functional theory for a series of heterocyclic polyacenes. Available X-ray structures of bis-triazines are compared to computed model compounds and used to check the methodology. A hexacyclic bis-1,2,4-triazine is predicted to have a triplet ground state.