A384107 Number of connected components of n faces of the icosidodecahedron up to the 120 rotations and reflections of the icosidodecahedron.

1, 2, 1, 3, 7, 18, 49, 140, 400, 1173, 3398, 9647, 26437, 67979, 159964, 334197, 602603, 910750, 1134215, 1153652, 963091, 664159, 382949, 185074, 75612, 25829, 7472, 1766, 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 icosidodecahedron is the polyhedral dual of the rhombic triacontahedron.

Links

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

Peter Kagey, Illustration of a(1)-a(4).

Wikipedia, Icosidodecahedron

Example

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

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: A294620 A010758 A259419 * A019224 A298096 A053190

Adjacent sequences: A384104 A384105 A384106 * A384108 A384109 A384110

Keyword

nonn,fini,full

Author

Peter Kagey, May 20 2025

Extensions

a(12)-a(32) from Bert Dobbelaere, May 24 2025

Status

approved