Figure presents the distribution of the dimensionality of nets identified in the Materials Project database. We can see that 3.9% of the structures are aperiodic, i.e., corresponds to clusters of atoms unconnected through space. 4.5% of the MP structures feature onedimensional nets: these are typically linear chains of atoms, a net we call in this work the rod topology. Out of the 6420 one-dimensional nets identified, 6091 are rod nets; the remaining 329 correspond to more complex one-dimensional nets (103 different types of 1D nets are represented). 2D nets represent 10.5% of the MP structures, and will be discussed in more detail in section . We focus in the rest of this section on three-dimensional nets, which represent the large majority of the MP database, with 81.1% of structures. The first thing we want to highlight from this analysis is the very large diversity of topology that is encountered through the Materials Project database. In fact, the 134,500 materials with 3D nets are distributed into 38,430 different topologies, an average of ≈3.5 materials per topology. But the distribution is very unbalanced, with a fat-tailed nature: the most common topology (pcu) is encountered 8513 times, and the 20 most common topologies together account for 37,579 materials (27.9% of the database). On the other hand, the the vast majority (29,185) of net topologies occur only once in the database. This huge diversity of the topologies encountered can be surprising or counter-intuitive to solid-state chemists, who like to classify materials in well-known topologies (for example, for common minerals). However, the need for increasing topological diversity in databases of hypothetical materials has been highlighted before, for example by Anderson et al. in the case of metal-organic frameworks (MOFs). We believe our present analysis reinforces this point: computational databases generated by enumeration of a limited number of identified topologies are inherently limited compared to the wide diversity observed here.