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

Author

Peter Kagey, May 18 2025

Keywords

• nonn
• fini
• full

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.

Examples

			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.
		

Links

• Peter Kagey, Illustration of a(1)-a(3).
• Wikipedia, Truncated cuboctahedron

Crossrefs

Cf. A383806 (disdyakis dodecahedron).

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

Extensions

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