cp's OEIS Frontend

We can subdivide the 230 crystallographically permissible 3D space groups into 16 subsets based on the number of general positions (i.e., coordinate triplets whose values describe points occupied by symmetry-equivalent atoms in 3D space) specified by the symmetry operators in each subset. These numbers range from 1 (corresponding to exclusively one primitive triclinic space group, P1) to 192 (corresponding to the four face-centered cubic space groups Fm-3m, Fm-3c, Fd-3m, and Fd-3c). Multiplicities 1 and 9 (corresponding to exclusively one rhombohedral space group, R3h) represent the smallest subsets, whereas the largest subset is formed by the 63 space groups with multiplicity 8.