This section is dedicated to see the embeddings by CLICS. In section 4.1, the retrieval accuracies of 228 space groups and 233 local atomic environments (Table in the supplementary information) are evaluated. Some examples are discussed in detail. The accuracy of retrieving 5166 full patterns of polyhedral connections was not evaluated, because the intra-categories are too fine to be rigorously matched. A detailed analysis for the connected geometries is provided in the supplementary information. Section 4.2 shows the relationships among geometric concepts acquired by CLICS. Section 4.3 and 4.4 demonstrate that CLICS has integrally embedded the geometric concepts, through similar structure search, and by showing noticeable improvements on few-shot/imbalanced crystal structure classification tasks.