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 A385271 #12 Jun 26 2025 01:17:08 %S A385271 1,1,2,3,9,17,60,166,606,2106,8046,30801,122442,491539,2007571, %T A385271 8272122,34408439,144084776,607112043,2571118048,10938419260, %U A385271 46720437135 %N A385271 Number of face-connected components of square pyramidal cells in the hexakis cubic honeycomb up to translation, rotation, and reflection of the honeycomb. %C A385271 These are "free polyforms" because they are counted up to rotation and reflection. %C A385271 The "hexakis cubic honeycomb" is also called the "pyramidille" and is dual to the truncated cubic honeycomb. %C A385271 The square pyramidal cells are similar to the convex hull of (0,0,0), (2,0,0), (0,2,0) (2,2,0), and (1,1,1). %H A385271 Peter Kagey, <a href="/A385271/a385271.gif">Animation illustrating the a(5)=17 connected 5-cell components</a>. %H A385271 Wikipedia, <a href="https://en.wikipedia.org/wiki/Architectonic_and_catoptric_tessellation">Architectonic and catoptric tessellation</a> %H A385271 Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetragonal_disphenoid_honeycomb#Hexakis_cubic_honeycomb">Tetragonal disphenoid honeycomb</a>, see section "Hexakis cubic honeycomb." %Y A385271 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 A385271 nonn,hard,more %O A385271 0,3 %A A385271 _Peter Kagey_ and _Bert Dobbelaere_, Jun 25 2025