A384110 Number of connected components of n faces of the rhombicosidodecahedron up to the 120 rotations and reflections of the rhombicosidodecahedron.

1, 3, 2, 6, 13, 43, 125, 442, 1498, 5393, 19187, 69186, 248111, 888783, 3159624, 11137858, 38773614, 132891874, 446478045, 1463990116, 4662369227, 14350218212

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 rhombicosidodecahedron is the polyhedral dual of the deltoidal hexecontahedron.

Links

Table of n, a(n) for n=0..21.

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

Wikipedia, Rhombicosidodecahedron.

Example

a(1) = 3 because the rhombicosidodecahedron is not face transitive, but has three distinct orbits of faces: (1) triangles, (2) squares, and (3) 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: A078091 A073883 A248982 * A382395 A333446 A289069

Adjacent sequences: A384107 A384108 A384109 * A384111 A384112 A384113

Keyword

nonn,fini,more

Author

Peter Kagey, May 20 2025

Extensions

a(11)-a(21) from Bert Dobbelaere, May 26 2025

Status

approved