cylindrical pores that run parallel to each other. The pore structure of PCOD8331112 is a 3-dimensional network that is formed of two types of connected spherical cavities. The 0-D barcodes of both structures start with as many intervals as there are points sampled on the pore surfaces. More information is contained in the long intervals describing robust shape features: the existence of the single long interval in its 0-D barcode implies that the pore system of PCOD8331112 is connected. In contrast, the pore system of DON consists of eight unconnected components, encoded by the eight long intervals in its 0-D barcode. The 1-D and 2-D barcodes contain information on the shape of the cavities (see SI section \[theo\] for details).

The most elementary, but highly non-trivial, application of our approach is to identify porous materials with similar pore structures. As we have a database of over 3,000,000 nanoporous structures,[@sim151] visual inspection is out of question. Suppose we would like to know whether the library of hypothetical zeolites contains structures whose pore geometry is similar to a given material, e.g., a synthesized zeolite. To see the effectiveness of our approach, it is instructive to take a structure and find the four 