The obtained AE dictionary contains a total of 47 different SOAP environments. Figure shows the 12 ones typical of icosahedral Au NPs, organized hierarchically in a dendrogram based on their SOAP distance and similarity (see Methods). Figure shows the dendrogram containing the 22 environments characteristic of the decahedral Au NP. Figure shows the dendrogram of the 13 SOAP AEs typical of truncated-octahedral and cuboctahedral NPs. Finally, Figure shows the complete SOAP dictionary, containing all AEs proper of Ih, Dh and To Au NPs, organized based on their SOAP distance and similarity (see Methods). Such a dictionary of SOAP spectra can be then used to compare and classify the AEs that emerge along the MD simulations of a given NP, and to understand if on that specific NP AEs emerge which are closer to those present in NPs of other shapes. While the dendrogram of Figure contains the complete information, this also shows, e.g., that most of the bulk environments across different-shape NPs are basically identical to each other. Thus, to ensure to capture of relevant variations in our analysis, we opted to "truncate" the dendrogram at the distance of d SOAP = 0.08 (and considering as relevant only differences larger than this). This reduces the 47 AEs to 10 AEs, improving the clarity and the statistical relevance of the subsequent analysis. Nonetheless, the resolution of such analysis can be in principle adapted, based on the relevance of the difference between the AEs. This "cut" provides a coarse-grained analysis, which regroups all AEs with d SOAP < 0.08 in macro-clusters all SOAP environments