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.

1, 1, 2, 9, 57, 460, 4641, 50353, 575375, 6754382, 80887484, 982952256, 12087512169

Offset: 0

Author

Peter Kagey and Bert Dobbelaere, Jun 25 2025

Keywords

• nonn
• hard
• more

Comments

These are "free polyforms" because they are counted up to rotation and reflection.

The trapezo-rhombic dodecahedral honeycomb is dual to the gyrated tetrahedral-octahedral honeycomb.

Links

• Peter Kagey, Animation illustrating the a(4)=57 connected 4-cell components.
• Wikipedia, Rhombic dodecahedral honeycomb, see section "Trapezo-rhombic dodecahedral honeycomb."
• Wikipedia, Trapezo-rhombic dodecahedron

Crossrefs

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).