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 A385267 #15 Jun 26 2025 01:17:30 %S A385267 1,1,3,4,13,29,106,331,1222,4390,16588,62865,243217,947711,3732800, %T A385267 14801687,59103268,237305379,957738244,3882631356,15804400624 %N A385267 Number of face-connected components of half pyramidille cells in the half pyramidille up to translation, rotation, and reflection of the honeycomb. %C A385267 The half pyramidille is the dual to the cantitruncated tetrahedral-octahedral honeycomb (also known as the runcicantic cubic honeycomb) which consists of truncated cuboctahedra, truncated cubes and truncated tetrahedra. %C A385267 Each cell is similar to the convex hull of (0,0,0), (2,0,0), (2,2,0), and (1,1,1). %H A385267 Peter Kagey, <a href="/A385267/a385267.gif">Animation illustrating the a(4) = 13 connected components consisting of 4 cells</a>. %H A385267 Wikipedia, <a href="https://en.wikipedia.org/wiki/Architectonic_and_catoptric_tessellation">Architectonic and catoptric tessellation</a> %H A385267 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetrahedral-octahedral_honeycomb#Runcicantic_cubic_honeycomb">Tetrahedral-octahedral honeycomb</a> (see subsection "Runcicantic cubic honeycomb.") %Y A385267 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 A385267 nonn,hard,more %O A385267 0,3 %A A385267 _Peter Kagey_ and _Bert Dobbelaere_, Jun 23 2025