applications of topological data analysis that requires persistent homology in three different dimensions.

[**Acknowledgements**]{} This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 666983 and No 339025), the National Center of Competence in Research (NCCR) ‘ Materials’ Revolution: Computational Design and Discovery of Novel Materials (MARVEL)’ of the Swiss National Science Foundation (SNSF), and the Center for Gas Separations Relevant to Clean Energy Technologies, an Energy Frontier Research Center funded by the DOE, Office of Science, Office of Basic Energy Sciences under award DE-SC0001015 (a detailed acknowledgment is given in the SI).

[**Additional information**]{} Supplementary information is available in the online version of the paper. Reprints and permissions information is available at www.nature.com /reprints. Readers are welcome to comment on the online version of the paper. Correspondence and requests for materials should be addressed to B.S.(berend.smit@epfl.ch).

[**Competing financial interests**]{} The authors declare no competing financial interests.

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Fig. 1. [**Examples of fingerprints obtained by persistent homology for two different zeolite structures DON (top) and PCOD8331112 (bottom).**]{} The figures on the left show the structures, the middle the fingerprints, and the right 