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 A385274 #10 Jun 26 2025 01:16:52 %S A385274 1,1,2,4,14,43,197,850,4154,20371,103405,530355,2760533,14499363, %T A385274 76842876,410164367,2203491401,11903591737 %N A385274 Number of face-connected components of rhombic pyramidal cells in the rhombic pyramidal honeycomb up to translation, rotation, and reflection of the honeycomb. %C A385274 These are "free polyforms" because they are counted up to rotation and reflection. %C A385274 The "rhombic pyramidal honeycomb" is also called the "half oblate octahedrille" and is dual to the cantic cubic honeycomb, which is also called the "truncated tetraoctahedrille" or the "truncated tetrahedral-octahedral honeycomb" %C A385274 The rhombic pyramidal cells are similar to the convex hull of (0,0,0), (1,1,1), (1,1,-1), (0,2,0), and (2,0,0). %H A385274 Peter Kagey, <a href="/A385274/a385274.gif">Animation illustrating the a(4)=14 connected 4-cell components</a>. %H A385274 Wikipedia, <a href="https://en.wikipedia.org/wiki/Architectonic_and_catoptric_tessellation">Architectonic and catoptric tessellation</a> %H A385274 Wikipedia, <a href="https://en.wikipedia.org/wiki/Rhombic_dodecahedral_honeycomb#Rhombic_pyramidal_honeycomb">Rhombic dodecahedral honeycomb</a>, see section "Rhombic pyramidal honeycomb." %Y A385274 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 A385274 nonn,hard,more %O A385274 0,3 %A A385274 _Peter Kagey_ and _Bert Dobbelaere_, Jun 25 2025