A384111 Number of connected components of n faces of the truncated icosidodecahedron up to the 120 rotations and reflections of the truncated icosidodecahedron.

1, 3, 3, 12, 38, 167, 731, 3504, 16734, 81247, 392387, 1886246, 8958474, 41841440, 190731843, 841422704, 3558291221, 14287757043

Offset: 0

Author

Peter Kagey, May 20 2025

Keywords

• nonn
• fini
• more

Comments

Two faces are connected if they share an edge.

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

The truncated icosidodecahedron is the polyhedral dual of the disdyakis triacontahedron.

Examples

			a(1) = 3 because the truncated icosidodecahedron is not face transitive, but has three distinct orbits of faces: (1) squares, (2) hexagons, and (3) decagons.
		

Links

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

Crossrefs

Cf. A384067 (cuboctahedron), A384068 (truncated cube), A384069 (truncated octahedron), A384070 (rhombicuboctahedron), A384071 (cuboctahedron), A384072 (snub cube), A384104 (truncated tetrahedron), A384107 (icosidodecahedron), A384108 (truncated dodecahedron), A384109 (truncated icosahedron), A384110 (rhombicosidodecahedron), A384111 (truncated icosidodecahedron), A384112 (snub dodecahedron).

Extensions

a(9)-a(17) from Bert Dobbelaere, May 26 2025