Higher dimensional features of the PEL are not without chemical relevance and there is a distinct need for compact representations that encode them. Second-order saddles are well-established and there is growing evidence that some reactions follow such paths from ab-initio molecular dynamics. At the same time, there is growing interest to be able to more clearly connect the additive contributions to the energy landscape and the resulting global topology. As an alternative to disconnectivity graphs, in recent work we introduced sublevelset persistent homology as an efficient quantitative descriptor of high-dimensional energy landscapes. The sublevelset persistent homology barcode representation of a PEL includes the lower-dimensional topological features measured by disconnectivity graphs, as well as higher-dimensional information. We further developed a mathematical platform for using the patterns in a persistence barcode to predict the topological features of an energy landscape given certain criterion. Specifically, for the conformational energy landscape of chain-alkane molecules, we demonstrated that the additive nature of the intramolecular potential energy allowed use of the Künneth formula from mathematics in order to describe the topological features in terms of the simpler building blocks that are added together. This included the number of persistent homology bars, as well as their birth and death values. The Künneth formula leverages the symmetry of the PEL -for example, explaining how the topological features of building block units of an alkane embed as the number of carbons is increased.