A385268 Number of face-connected components of oblate cubille cells in the oblate cubille up to translation, rotation, and reflection of the honeycomb.

1, 1, 1, 3, 7, 24, 93, 427, 2043, 10412, 54072, 287121, 1543567, 8393603, 46040030, 254484780, 1415837030, 7922633039

Offset: 0

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

• nonn
• hard
• more

Comments

These are "free polyforms" because two connected components are considered to be the same if one can be rotated or reflected to match the other.

Each cell is 1/4 of a rhombic dodecahedron, and is similar to the convex hull of (-1,1,1), (0,0,0), (0,0,2), (0,2,0), (1,-1,1), (1,1,-1), (1,1,1), and (2,0,0).

The "oblate cubille" is also called the "trigonal trapezohedral honeycomb."

Links

• Peter Kagey, Animation illustrating the a(5)=24 connected 5-cell components.
• Wikipedia, Architectonic and catoptric tessellation
• Wikipedia, Trigonal trapezohedral honeycomb

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).