A384067 -id:A384067 - cp's OEIS frontend

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

Peter Kagey, May 20 2025

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.

			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.

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

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).

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

A384112 Number of connected components of n faces of the snub dodecahedron up to the 60 rotations of the snub dodecahedron.

Original entry on oeis.org

1, 3, 3, 6, 19, 51, 157, 465, 1444, 4492, 14236, 45097, 143753, 458400, 1464997, 4682469, 14970906, 47834908, 152721958, 486927066, 1549733096, 4920704208, 15579074400

Offset: 0

Peter Kagey, May 20 2025

Two faces are connected if they share an edge.
These are "one-sided" polyforms because rotations are allowed but reflections are not allowed.
The snub dodecahedron is the polyhedral dual of the pentagonal hexecontahedron.

			a(1) = 3 because the snub dodecahedron is not face transitive, but has three distinct orbits of faces: (1) pentagons, (2) triangles that are connected to a pentagon, and (3) triangles that are not connected to a pentagon.

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

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

cp's OEIS Frontend

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

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