cp's OEIS Frontend

A385276 Number of face-connected components of trapezo-rhombic dodecahedral cells in the trapezo-rhombic dodecahedral honeycomb up to translation, rotation, and reflection of the honeycomb.

%I A385276 #10 Jun 26 2025 01:16:43
%S A385276 1,1,2,9,57,460,4641,50353,575375,6754382,80887484,982952256,
%T A385276 12087512169
%N A385276 Number of face-connected components of trapezo-rhombic dodecahedral cells in the trapezo-rhombic dodecahedral honeycomb up to translation, rotation, and reflection of the honeycomb.
%C A385276 These are "free polyforms" because they are counted up to rotation and reflection.
%C A385276 The trapezo-rhombic dodecahedral honeycomb is dual to the gyrated tetrahedral-octahedral honeycomb.
%H A385276 Peter Kagey, <a href="/A385276/a385276.gif">Animation illustrating the a(4)=57 connected 4-cell components</a>.
%H A385276 Wikipedia, <a href="https://en.wikipedia.org/wiki/Rhombic_dodecahedral_honeycomb#Trapezo-rhombic_dodecahedral_honeycomb">Rhombic dodecahedral honeycomb</a>, see section "Trapezo-rhombic dodecahedral honeycomb."
%H A385276 Wikipedia, <a href="https://en.wikipedia.org/wiki/Trapezo-rhombic_dodecahedron">Trapezo-rhombic dodecahedron</a>
%Y A385276 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 A385276 nonn,hard,more
%O A385276 0,3
%A A385276 _Peter Kagey_ and _Bert Dobbelaere_, Jun 25 2025