Whereas prior approaches to constitutional isomerism focused on the number of isomers for a given set of atoms, we asked the broader question: how do the isomers interconvert? To this end, we adapted the principles of the Polytope Formalism (as applied to stereoisomerism) to constitutional isomerism generating mathematically comprehensive structured lists of atomconnectivity configuration species (Fig. ). As the approach explicitly includes subvalent and hypervalent configurations, it generates species corresponding to isomerization intermediates. The configuration lists are highly structured and form discrete configuration spaces that encode the inter-configuration relationships. The configuration spaces map onto PESs and hence the graph representation of the configuration spaces provide compact descriptions of the associated PESs. Requisite terminology and a taxonomic system reflecting this configuration space structure was implemented.