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 A385268 #16 Jun 26 2025 01:17:22 %S A385268 1,1,1,3,7,24,93,427,2043,10412,54072,287121,1543567,8393603,46040030, %T A385268 254484780,1415837030,7922633039 %N A385268 Number of face-connected components of oblate cubille cells in the oblate cubille up to translation, rotation, and reflection of the honeycomb. %C A385268 These are "free polyforms" because two connected components are considered to be the same if one can be rotated or reflected to match the other. %C A385268 Each cell is 1/4 of a rhombic dodecahedron, and is similar to the convex hull of (-1,1,1), (0,0,0), (0,0,2), (0,2,0), (1,-1,1), (1,1,-1), (1,1,1), and (2,0,0). %C A385268 The "oblate cubille" is also called the "trigonal trapezohedral honeycomb." %H A385268 Peter Kagey, <a href="/A385268/a385268.gif">Animation illustrating the a(5)=24 connected 5-cell components</a>. %H A385268 Wikipedia, <a href="https://en.wikipedia.org/wiki/Architectonic_and_catoptric_tessellation">Architectonic and catoptric tessellation</a> %H A385268 Wikipedia, <a href="https://en.wikipedia.org/wiki/Trigonal_trapezohedral_honeycomb">Trigonal trapezohedral honeycomb</a> %Y A385268 Cf. A038119 (cubic), A038173 (rhombic dodecahedral), A038181 (truncated octahedral), A343909 (tetrahedral-octahedral), A365654 (square bipyramidal), A384254 (rectified cubic), A384274 (quarter cubic), A384754 (omnitruncated cubic), A385024 (tetragonal disphenoidal), A385025 (gyrobifastigium), A385026 (hexagonal prismatic), A385027 (triakis truncated tetrahedral), A385267 (half pyramidille), A385268 (oblate cubille), A385269 (quarter cubille), A385270 (elongated dodecahedral), A385271 (hexakis cubic), A385272 (phyllic disphenoidal), A385273 (quarter oblate octahedrille), A385274 (rhombic pyramidal), A385275 (square quarter pyramidille), A385276 (trapezo-rhombic dodecahedral), A385277 (triangular prismatic). %K A385268 nonn,hard,more %O A385268 0,4 %A A385268 _Peter Kagey_ and _Bert Dobbelaere_, Jun 23 2025