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

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

Offset

0,2

Comments

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.

Links

Table of n, a(n) for n=0..22.

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

Wikipedia, Snub dodecahedron.

Example

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.

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: A025256 A052560 A147836 * A391830 A284710 A377146

Adjacent sequences: A384109 A384110 A384111 * A384113 A384114 A384115

Keyword

nonn,fini,more

Author

Peter Kagey, May 20 2025

Extensions

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

Status

approved