A384072 Number of connected components of n faces of the snub cube up to the 24 rotations of the snub cube.

1, 3, 3, 6, 16, 39, 101, 263, 694, 1839, 4884, 12840, 33508, 86227, 218284, 538796, 1284335, 2919365, 6249499, 12411396, 22483152, 36410533, 51641029, 62911551, 64827047, 55869657, 40009946, 23732630, 11668877, 4763611, 1619236, 456756, 106602, 20157, 3101, 358, 37, 3, 1

Offset

0,2

Comments

Two faces are connected if they share an edge.

These are "one-sided" polyforms because reflections are not allowed.

The snub cube is the polyhedral dual of the pentagonal icositetrahedron.

Links

Table of n, a(n) for n=0..38.

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

Wikipedia, Snub cube

Example

a(1) = 3 because the snub cube is not face transitive, but has three distinct orbits of faces: (1) squares, (2) triangles that are connected to a square, and (3) triangles that are not connected to a square.

Crossrefs

Cf. A383808 (pentagonal icositetrahedron).

Cf. A309159 (snub square tiling), A383908 (snub trihexagonal tiling).

Cf. A384067 (cuboctahedron), A384068 (truncated cube), A384069 (truncated octahedron), A384070 (rhombicuboctahedron), A384071 (truncated cuboctahedron), A384072 (snub cube).

Sequence in context: A348539 A095356 A123104 * A038076 A123286 A132818

Adjacent sequences: A384069 A384070 A384071 * A384073 A384074 A384075

Keyword

nonn,fini,full

Author

Peter Kagey, May 18 2025

Extensions

a(13)-a(38) from Bert Dobbelaere, May 24 2025

Status

approved