For a full listing of the atom-connectivity species examples arising from application of the formalism for this system (Fig. ), including some density-functional theory (DFT) geometries, see the Supplementary Information. Integrability of the formalism with cheminformatic tools. In chemical databases (e.g., the CAS database) that provide structure and substructure search features, the structures are stored and processed as bonding matrices, that is, they are digitally represented as atom-connectivity lists augmented by bond multiplicities and stereodescriptors. Also, systematic chemical names are automatically generated from the same digital representation. The atom-connectivity permuted structures generated by the Polytope Formalism of constitutional isomerism (or its focused 𝒮 𝑚 ℬ 𝑛 partitioned approach) provide descriptions of "structures" that are compatible with these databases and functionality. Consequently, many existing cheminformatics tools are expected to be readily adaptable to the implementation of the principles and concepts described here.