A384109 Number of connected components of n faces of the truncated icosahedron up to the 120 rotations and reflections of the truncated icosahedron.

1, 2, 2, 5, 14, 41, 135, 461, 1610, 5564, 18769, 59513, 173692, 448720, 993666, 1820321, 2700927, 3225519, 3146565, 2555112, 1761447, 1041034, 531851, 234072, 88977, 28779, 7997, 1837, 378, 62, 12, 2, 1

Offset: 0

Author

Peter Kagey, May 20 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 icosahedron is the polyhedral dual of the pentakis dodecahedron.

Examples

			a(1) = 2 because the truncated dodecahedron is not face transitive, but has two distinct orbits of faces: (1) pentagons and (2) hexagons.
		

Links

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

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