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

Author

Peter Kagey, May 23 2025

Keywords

• nonn
• more
• hard

Comments

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

Examples

			For n=1, the a(1)=2 different components are the cuboctahedron and the octahedron.
For n=2, the a(2)=1 component is a cuboctahedron connected to an octahedron.
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.
		

Links

• Peter Kagey, Illustration of a(3)=9.
• Wikipedia, Convex uniform honeycomb

Crossrefs

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

Extensions

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