“…There are a plethora of crystal comparison algorithms currently available with a variety of methods ranging from reductions in the dimensionality of input structures into more manageable representations based on intrinsic properties (e.g., periodic point sets, crystallographic information, X-ray powder diffraction, etc.) to transformations of the crystallographic information into a many dimensional configurations (or fingerprint) space (Sadeghi et al, 2013;Valle & Oganov, 2010;Willighagen et al, 2005;Gelder et al, 2001;Karfunkel et al, 1993;Verwer & Leusen, 1998;Mosca & Kurlin, 2020;Thomas et al, 2021;Widdowson et al, 2022;Edelsbrunner et al, 2021;de la Flor et al, 2016;Ferré et al, 2015;Hicks et al, 2021;Gelato & Parthe, 1987;Dzyabchenko, 1994;Lonie & Zurek, 2012;Chuanxun et al, 2017;Ong et al, 2013). These methods can mitigate complexities that arise when dealing with a direct comparison of atomic positions (e.g., atom labeling, special positions, space group conversions, etc.).…”