A384108 Number of connected components of n faces of the truncated dodecahedron up to the 120 rotations and reflections of the truncated dodecahedron.

1, 2, 2, 7, 25, 92, 380, 1466, 5418, 17823, 52118, 132555, 294285, 566632, 950083, 1384788, 1760028, 1948075, 1881390, 1581334, 1157179, 733548, 402440, 189297, 76312, 25916, 7481, 1767, 370, 61, 12, 2, 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 dodecahedron is the polyhedral dual of the triakis icosahedron.

Links

Table of n, a(n) for n=0..32.

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

Wikipedia, Truncated dodecahedron

Example

a(1) = 2 because the truncated dodecahedron is not face transitive, but has two distinct orbits of faces: (1) triangles and (2) 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: A342644 A069101 A221648 * A138802 A292016 A350020

Adjacent sequences: A384105 A384106 A384107 * A384109 A384110 A384111

Keyword

nonn,fini,full

Author

Peter Kagey, May 20 2025

Extensions

a(10)-a(32) from Bert Dobbelaere, May 24 2025

Status

approved