with similar conventional descriptors (small $D_{CS}$) but the shapes of their pores can differ enormously (large $D_{TS}$). Figure \[4similar\]b shows two cases where the conventional approach identifies structures with very similar conventional descriptors (see SI Table \[StructProp\]) but very different pore structures. In contrast, if we use our topology-based fingerprint, we indeed retrieve structures that look strikingly similar. In the SI (section \[similarity\]) we show that one can also use this similarity search to compare structures from different classes of nanoporous materials. These findings are guaranteed by a stability theorem that is a key result in persistent homology:[@cha141] materials with similar shapes are described by similar barcodes.

For the traditional descriptors with geometric meaning, one expects to find correlations with information encoded in the persistent homological fingerprint (see SI Table \[BarcodeErrors\]). For example, the radius of the maximum included sphere is correlated with the 2-D barcode as the radius of a cavity determines the death time of an interval in the 2-D-barcode. Further geometric information, like the connectivity of the pore structure (0-D) or the number of independent tunnels (1-D), is also encoded in the persistence barcodes. Therefore, only the combination of the barcodes of all three dimensions captures the 