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 A385273 #9 Jun 26 2025 01:16:58 %S A385273 1,1,2,6,24,114,647,3883,24605,159837,1060450,7137627,48624639, %T A385273 334475495,2319909330,16205238283 %N A385273 Number of face-connected components of polyhedral cells in the quarter oblate octahedrille up to translation, rotation, and reflection of the honeycomb. %C A385273 These are "free polyforms" because they are counted up to rotation and reflection. %C A385273 The quarter oblate octahedrille is dual to the cantellated cubic honeycomb. %C A385273 The cells of the quarter oblate octahedrille are similar to the convex hull of (0,0,0), (1,0,0), (0, 1, 0), (1,1,1), and (1,1,-1). %H A385273 Peter Kagey, <a href="/A385273/a385273.gif">Animation illustrating the a(4)=24 connected 4-cell components</a>. %H A385273 Wikipedia, <a href="https://en.wikipedia.org/wiki/Architectonic_and_catoptric_tessellation">Architectonic and catoptric tessellation</a> %Y A385273 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 A385273 nonn,hard,more %O A385273 0,3 %A A385273 _Peter Kagey_ and _Bert Dobbelaere_, Jun 25 2025