A384254 Number of connected components of n polyhedra in the rectified cubic honeycomb up to translation, rotation, and reflection of the honeycomb.

1, 2, 2, 9, 40, 290, 2529, 26629, 301289, 3568048, 43305326, 534671742, 6684869463

Offset

0,2

Comments

Equivalently the number of connected components of n polyhedra in the truncated cubic honeycomb up to translation, rotation, and reflection of the honeycomb.

Links

Table of n, a(n) for n=0..12.

Bert Dobbelaere, Peter Kagey, Drake Thomas, and Andrés R. Vindas-Meléndez, Building with Blocks: Enumerating Polyforms on Tilings, arXiv:2602.23301 [math.CO], 2026. See pp. 8-9.

Peter Kagey, Illustration of a(3)=9.

Wikipedia, Convex uniform honeycomb

Example

For n=1, the a(1)=2 different components are the cuboctahedron and the octahedron.
For n=2, the a(2)=2 different components are a cuboctahedron connected to an octahedron and two cuboctahedra connected along their square faces.
For n=3, there are A000162(3)=2 components that consist of three cuboctahedra, four connected components that consist of two cuboctahedra and an octahedron, and three components that consist of a cuboctahedron and two octahedra.

Crossrefs

Cf. A038119 (cubic honeycomb), A038181 (bitruncated cubic honeycomb), A343577 (truncated square tiling), A343909 (tetrahedral-octahedral honeycomb), A384274 (rectified cubic honeycomb).

Sequence in context: A205390 A204265 A343406 * A081086 A019514 A135816

Adjacent sequences: A384251 A384252 A384253 * A384255 A384256 A384257

Keyword

nonn,more,hard

Author

Peter Kagey, May 23 2025

Extensions

a(8)-a(12) from Bert Dobbelaere, Jun 09 2025

Status

approved