Eumelanin is responsible for photoprotection in living organisms. It is made of 5,6-dihydroxyindole (DHI) oligomers. However, lack of detailed structural knowledge limits understanding its function and exploiting its potential in material science. To uncover the relationship between structural stability and optical properties, we have studied a virtual library of minimal oligomer models made of 830 DHI dimers. We find a preference for oxidized, polycyclic structures which speaks in favor of graphite-like structures for the larger oligomers, and propose an electrocyclic formation mechanism. Besides widely considered quinone oxidation patterns, also structures with one or three oxidized sites per fragment and an interfragment double bond are stable, and we introduce a new representative set of 49 stable dimers that considers this diversity. Some stable oxidized dimers have absorption energies as low as 1.3 eV. They may be present as substructures in the naturally found oligomers and contribute to the absorption spectrum of the biopolymer.