Fundamental difference that exists between synthetic versus analytic chemical nomenclature

A problem of a fundamental nature in the assignment of a consistent expandable system of chemical nomenclature is that every ''synthetic'' nomenclature algorithm will eventually, as the allowable permutation of atoms and means of connecting them (i.e., bonds) grows large, produce internal contradictions. This forces setting of limitations to the indiscriminate use of any synthetic system for canonically naming a given molecule. Although such a problem does not arise for an ''analytical'' algorithm, by definition, such a system is not expandable. A geometrical analog which underlies this problem is noted in an examination of the smallest geometric entity that involves ''shape'' (the simplex in two dimensions) and the implications to chemistry in the topological difference that exists between SAS and ASA triangle comparisons.