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

0,2

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.

Links

Table of n, a(n) for n=0..17.

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

Wikipedia, Truncated icosidodecahedron.

Example

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.

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).

Sequence in context: A370145 A025236 A014432 * A107330 A382334 A076509

Adjacent sequences: A384108 A384109 A384110 * A384112 A384113 A384114

Keyword

nonn,fini,more

Author

Peter Kagey, May 20 2025

Extensions

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

Status

approved