cp's OEIS Frontend

A385278 Number of face-connected components of polyhedral cells in the triangular pyramidille up to translation, rotation, and reflection of the honeycomb.

%I A385278 #11 Jun 29 2025 10:08:40
%S A385278 1,1,3,4,16,39,152,517,2056,8002,32692,134198,561511,2366909,10075926,
%T A385278 43174057,186208658,807426463,3518610508,15400996653
%N A385278 Number of face-connected components of polyhedral cells in the triangular pyramidille up to translation, rotation, and reflection of the honeycomb.
%C A385278 These are "free polyforms" because they are counted up to rotation and reflection.
%C A385278 The triangular pyramidille is dual to the cantitruncated cubic honeycomb.
%C A385278 The polyhedral cells are each 1/24 of a cube and are similar to the convex hull of (0,0,0), (2,0,0), (1,1,0), and (1,1,1).
%H A385278 Peter Kagey, <a href="/A385278/a385278.gif">Animation illustrating the a(5)=39 connected 5-cell components</a>.
%H A385278 Wikipedia, <a href="https://en.wikipedia.org/wiki/Architectonic_and_catoptric_tessellation">Architectonic and catoptric tessellation</a>
%H A385278 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cubic_honeycomb#Triangular_pyramidille">Cubic honeycomb</a>
%Y A385278 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 A385278 nonn,hard,more
%O A385278 0,3
%A A385278 _Peter Kagey_ and _Bert Dobbelaere_, Jun 25 2025