Data-Driven Topological Analysis of Polymorphic Crystal Structures

Polymorphism, the ability of a compound to crystallize in multiple distinct structures, plays a vital role in determining the physical, chemical, and functional properties of polymorphic materials. While polymorphism enables many critical crystalline materials applications with special properties, predicting such polymorphic structures remains a big challenge. In this study, we analyze structural variations in the Materials Project database, including metastable and pressure-stabilized crystal structures, to explore the topological landscape of polymorphism. Using topological analysis, we identify key statistical patterns in composition, space-group distributions, and polyhedral building blocks. We discover that frequent space group pairs, such as (71,225), display consistent topological patterns across different compounds. We further show that, local polyhedral environments are often conserved across diverse structural variants of a given formula, even as global symmetry and packing arrangements change. By embedding these structures into a topological vector space, we show that structures can cluster together independent of their space group labels. Validation against experimental data from the ICSD confirms that these trends are physically real and not computational artifacts. These findings establish local topological identity as a more robust descriptor than space group symmetry for predicting and classifying structural diversity in inorganic polymorphic systems.