Networks of atom-centered coordination octahedra commonly occur in inorganic and hybrid solid-state materials. Characterizing their spatial arrangements and characteristics is crucial for relating structures to properties for many materials families. The traditional method using case-by-case inspection becomes prohibitive for discovering trends and similarities in large datasets. Here, we operationalize chemical intuition to automate the geometric parsing, quantification, and classification of coordination octahedral networks. We find axis-resolved tilting trends in ABO$_{3}$ perovskite polymorphs, which assist in detecting oxidation state changes. Moreover, we develop a scale-invariant encoding scheme to represent these networks, which, combined with human-assisted unsupervised machine learning, allows us to taxonomize the inorganic framework polytypes in hybrid iodoplumbates (A$_x$Pb$_y$I$_z$). Consequently, we uncover a violation of Pauling's third rule and the design principles underpinning their topological diversity. Our results offer a glimpse into the vast design space of atomic octahedral networks and inform high-throughput, targeted screening of specific structure types.

翻译：以原子为中心的配位八面体网络普遍存在于无机和杂化固态材料中。表征其空间排列和特征对于建立众多材料家族的结构与性能关系至关重要。传统采用逐案例分析的方法在发现大型数据集中的趋势与相似性时变得不可行。在此，我们将化学直觉操作化，实现了配位八面体网络的几何解析、量化和分类自动化。我们在ABO$_{3}$钙钛矿多型体中发现了轴分辨倾斜趋势，有助于检测氧化态变化。此外，我们开发了一种尺度不变编码方案来表示这些网络，结合人工辅助的无监督机器学习，对杂化碘铅酸盐（A$_x$Pb$_y$I$_z$）中的无机骨架多型体进行分类。由此，我们揭示了泡利第三规则的违反情况及其拓扑多样性背后的设计原理。我们的结果揭示了原子八面体网络的广阔设计空间，并为高通量、针对性筛选特定结构类型提供了参考。