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 A385272 #10 Jun 26 2025 01:17:02 %S A385272 1,1,2,4,13,38,141,515,2043,8176,33706,140471,593705,2531933,10893811, %T A385272 47202599,205843902,902644191,3977976135,17609163491 %N A385272 Number of face-connected components of phyllic disphenoidal cells in the phyllic disphenoidal honeycomb up to translation, rotation, and reflection of the honeycomb. %C A385272 These are "free polyforms" because they are counted up to rotation and reflection. %C A385272 The "phyllic disphenoidal honeycomb" is also called the "eighth pyramidille," and its dual is the omnitruncated cubic honeycomb. %C A385272 The phyllic disphenoidal cells are similar to the convex hull of (0,0,0), (1,0,0), (1,1,0), and (1,1,1). %H A385272 Peter Kagey, <a href="/A385272/a385272.gif">Animation illustrating the a(5)=38 connected 5-cell components</a>. %H A385272 Wikipedia, <a href="https://en.wikipedia.org/wiki/Architectonic_and_catoptric_tessellation">Architectonic and catoptric tessellation</a> %H A385272 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetragonal_disphenoid_honeycomb#Phyllic_disphenoidal_honeycomb">Tetragonal disphenoid honeycomb</a>, see section "Phyllic disphenoidal honeycomb." %Y A385272 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 A385272 nonn,hard,more %O A385272 0,3 %A A385272 _Peter Kagey_ and _Bert Dobbelaere_, Jun 25 2025