of geometric similarity by using topological data analysis (TDA). TDA is a field of big-data analysis that builds on techniques from algebraic topology, most noticeably persistent homology.[@ede101] Its guiding philosophy is that the ‘shape’ of the data reveals important information about the data.[@car091]

To assign a geometric descriptor to a given material, we sample points on the pore surface. By growing balls stepwise around each sample point and monitoring their pairwise overlaps, we compute the associated filtered Vietoris-Rips complex (see SI section \[theo\]), which is then characterized by its 0-, 1- and 2-dimensional homology classes. We store the lifetime of each homology class in the corresponding persistence barcode. Combining the 0-, 1-, and 2-dimensional barcodes yields a fingerprint that characterizes the overall shape of the pore structure.

For analyzing pore shapes we are in the unusually fortunate situation that, unlike most other big-data applications of persistent homology, our data have actual geometric meaning. In almost all known big-data applications only the 0-D and 1-D barcodes are of relevance, while here the 2-D barcodes also carry essential information. For example, figure \[DONh\] shows the fingerprints of two different zeolite structures, IZA zeolite DON and hypothetical zeolite PCOD8331112. DON contains eight identical 