This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381103 #24 May 01 2025 17:54:47 %S A381103 1,2,3,4,6,8,9,12,16,18,24,32,36,48,96,192 %N A381103 Number of permissible general positions in three-dimensional space groups obeying the crystallographic restriction theorem. %C A381103 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. %H A381103 B. Kahr, <a href="https://doi.org/10.1107/S2056989023000786">A periodic-like table of space groups</a>, Acta Cryst. E79, 124-128 (2023). %H A381103 B. Souvignier, H. Wondratschek, M. I. Aroyo, G. Chapuis, and A. M. Glazer, <a href="https://onlinelibrary.wiley.com/iucr/itc/Ac/ch1o4v0001/">International Tables for Crystallography Vol. A, Chapter 1.4</a>, pp. 42-73 (2015). [<a href="https://doi.org/10.1107/97809553602060000922">alternative link</a>] %Y A381103 Cf. A323383 (analog for the wallpaper groups). %Y A381103 Cf. A004028, A004029, A006227. %K A381103 nonn,fini,full %O A381103 1,2 %A A381103 _Ambarneil Saha_, Apr 14 2025