 The systematic and comprehensive nature of the outputs mathematically guarantee that nothing is missing.  The structure of the configuration spaces map onto PESs (they are isomorphic) and hence describe the corresponding elementary mechanisms.  The configuration spaces are "maps of", or "guides to" the different aspects of chemical space; the outputs of the formalism both define and describe chemical space in a rigorous and meaningful way. The approach presented here can generate the complete angular configuration space for arbitrary ABn. For AB4, the remaining angular displacements correspond to the triply degenerate T-4 T2-mode. These give the "AB4 T-4 T2-mode" configuration space which has the topology of a 3-sphere S 3 (hypersphere). The mathematically complete polytopal rearrangement configuration space for AB4 is thus the Cartesian product of these spaces, i.e., the AB4 T-4 (E T2)-mode space. It is the 5-dimensional hypersphere (S 5 ) topological manifold.