A385273 Number of face-connected components of polyhedral cells in the quarter oblate octahedrille up to translation, rotation, and reflection of the honeycomb.

1, 1, 2, 6, 24, 114, 647, 3883, 24605, 159837, 1060450, 7137627, 48624639, 334475495, 2319909330, 16205238283

Offset

0,3

Comments

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

The quarter oblate octahedrille is dual to the cantellated cubic honeycomb.

The cells of the quarter oblate octahedrille are similar to the convex hull of (0,0,0), (1,0,0), (0, 1, 0), (1,1,1), and (1,1,-1).

Links

Table of n, a(n) for n=0..15.

Peter Kagey, Animation illustrating the a(4)=24 connected 4-cell components.

Wikipedia, Architectonic and catoptric tessellation

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).

Sequence in context: A068199 A189846 A189283 * A177522 A216717 A174072

Adjacent sequences: A385270 A385271 A385272 * A385274 A385275 A385276

Keyword

nonn,hard,more

Author

Peter Kagey and Bert Dobbelaere, Jun 25 2025

Status

approved