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 A385269 #13 Jun 26 2025 01:17:17 %S A385269 1,1,2,4,18,67,374,2063,12482,76835,486375,3119695,20275051,133031450, %T A385269 880300617,5866722906 %N A385269 Number of face-connected components of quarter cubille cells in the quarter cubille up to translation, rotation, and reflection of the honeycomb. %C A385269 These are "free polyforms" because they are counted up to rotation and reflection. %C A385269 The quarter cubille is the dual to the runcic cubic honeycomb (equivalently, the cantellated tetrahedral-octahedral honeycomb) which consists of rhombicuboctahedra, cubes, and tetrahedra. %C A385269 Each cell is similar to the convex hull of (0,2,2), (2,0,2), (2,2,0), (2,2,2), and (1,1,1). %H A385269 Peter Kagey, <a href="/A385269/a385269.gif">Animation illustrating the a(4)=18 connected 4-cell components</a>. %H A385269 Wikipedia, <a href="https://en.wikipedia.org/wiki/Architectonic_and_catoptric_tessellation">Architectonic and catoptric tessellation</a> %H A385269 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb#Quarter_cubille">Tetrahedral-octahedral honeycomb</a> (see subsection "Quarter cubille.") %Y A385269 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 A385269 nonn,hard,more %O A385269 0,3 %A A385269 _Peter Kagey_ and _Bert Dobbelaere_, Jun 23 2025