A384071 Number of connected components of n faces of the truncated cuboctahedron up to the 48 rotations and reflections of the truncated cuboctahedron.

1, 3, 3, 11, 28, 100, 319, 1114, 3538, 10313, 25470, 52474, 88257, 121329, 136282, 125885, 95956, 60675, 31943, 14009, 5123, 1549, 398, 84, 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 truncated cuboctahedron is the polyhedral dual of the disdyakis dodecahedron.

Links

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

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

Wikipedia, Truncated cuboctahedron

Example

a(1) = 3 because the truncated cuboctahedron is not face-transitive but has three distinct types of faces: square faces, hexagonal faces, and octagonal faces.

Crossrefs

Cf. A383806 (disdyakis dodecahedron).

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

Sequence in context: A322701 A124265 A163938 * A373393 A109937 A054101

Adjacent sequences: A384068 A384069 A384070 * A384072 A384073 A384074

Keyword

nonn,fini,full

Author

Peter Kagey, May 18 2025

Extensions

a(12)-a(26) from Bert Dobbelaere, May 22 2025

Status

approved