A384070 Number of connected components of n faces of the rhombicuboctahedron up to the 48 rotations and reflections of the rhombicuboctahedron.

1, 3, 2, 6, 11, 32, 72, 207, 530, 1434, 3575, 8475, 17814, 32643, 49583, 60964, 58922, 44513, 26397, 12494, 4791, 1493, 390, 83, 17, 3, 1

Offset

0,2

Comments

Two faces are connected if they share an edge.

These are "free" polyforms because both rotations and reflections are allowed.

The rhombicuboctahedron is the polyhedral dual of the deltoidal icositetrahedron.

Links

Table of n, a(n) for n=0..26.

Peter Kagey, Illustration of a(1)-a(3).

Wikipedia, Rhombicuboctahedron

Example

a(1) = 3 because the rhombicuboctahedron is not face-transitive but has three distinct types of faces: triangular faces, square faces that are connected to a triangular face, and square faces that are not connected to a triangular face.

Crossrefs

Cf. A383804 (deltoidal icositetrahedron).

Cf. A384067 (cuboctahedron), A384068 (truncated cube), A384069 (truncated octahedron), A384070 (rhombicuboctahedron), A384071 (truncated cuboctahedron), A384072 (snub cube).

Sequence in context: A340733 A095011 A274975 * A188621 A175182 A291221

Adjacent sequences: A384067 A384068 A384069 * A384071 A384072 A384073

Keyword

nonn,fini,full

Author

Peter Kagey, May 18 2025

Extensions

a(14)-a(26) from Bert Dobbelaere, May 22 2025

Status

approved