 Generation of complete sets of isomeric configurations.  Includes the relationships between the configurations.  In combination, these are the "configuration spaces".  The configuration spaces are highly structured, and a taxonomic system has been developed for their description.  In the cases of continuum configuration spaces, they can be discretised allowing for a discrete (finite) representation.  Discrete configuration spaces can be represented as graphs which encode all their relevant properties.  Nomenclatural systems for individual configurations double as elements of systematic chemical nomenclature.  Precise terminology is useful for unambiguous and concise descriptions. The Polytope Formalism provides four highly significant benefits: