Small aromatic ring systems are of central importance in the development of novel synthetic protein ligands. Here we generate a complete list of 24,847 such ring systems. We call this list and associated annotations VEHICLe, which stands for virtual exploratory heterocyclic library. Searches of literature and compound databases, using this list as substructure queries, identified only 1701 as synthesized. Using a carefully validated machine learning approach, we were able to estimate that the number of unpublished, but synthetically tractable, VEHICLe rings could be over 3000. However, analysis also shows that the rate of publication of novel examples to be as low as 5-10 per year. With this work, we aim to provide fresh stimulus to creative organic chemists by highlighting a small set of apparently simple ring systems that are predicted to be tractable but are, to the best of our knowledge, unconquered.