Rigorous treatment of polytopal rearrangements reveal surprising complexity of stereoisomerism configuration landscapes.

The Polytope Formalism provides four highly significant benefits: • The formalism provides a common and hence unifying framework for the many disparate aspects of isomerism. • 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.

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