As an illustrative example, Fig. shows a simulated cubic perovskite ABX3, and the first 8 groups of the corresponding GRID. From Fig. , the coordination number of each atom within the perovskite is readily apparent; as the first two groups are identical but different to the 3 rd group, one of the atoms (X) must have a coordination number of two. Similarly, the changes between 6 th and 7 th groups suggests a coordination number of six must be present (B). Whilst this sort of manual analysis becomes more challenging for complex or low-symmetry structures, the coordination number and local symmetry is inherently embedded within the GRID. This reduces the data loss in converting 3D coordinates into a 1D histograms compared with the RDF. It is worth noting, however, that summation of all GRID groups will recover the traditional RDF distribution. As a demonstration of the effectiveness of the GRID in quantifying structural similarity, we have constructed three test examples in order to investigate different aspects of structural similarity: 1) structures formed by the variable intergrowth of two sub-units; 2) changes due to atomic displacements such as at a phase transitions; and 3) the effect of lattice parameter variations. Between them these examples cover long-range structure, short-range variations and changes to overall symmetry, demonstrating the wide applicability of this descriptor to structural comparisons. While GRID focusses on the structural aspect of S-C space, we will show later in this manuscript that it can also be combined with a measure of compositional similarity.