cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

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

Original entry on oeis.org

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

Views

Author

Peter Kagey, May 20 2025

Keywords

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.

Examples

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

Links

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

A384108 Number of connected components of n faces of the truncated dodecahedron up to the 120 rotations and reflections of the truncated dodecahedron.

Original entry on oeis.org

1, 2, 2, 7, 25, 92, 380, 1466, 5418, 17823, 52118, 132555, 294285, 566632, 950083, 1384788, 1760028, 1948075, 1881390, 1581334, 1157179, 733548, 402440, 189297, 76312, 25916, 7481, 1767, 370, 61, 12, 2, 1
Offset: 0

Views

Author

Peter Kagey, May 20 2025

Keywords

Comments

Two faces are connected if they share an edge.
These are "free" polyforms because both rotations and reflections are allowed.
The truncated dodecahedron is the polyhedral dual of the triakis icosahedron.

Examples

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

Links

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

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

Original entry on oeis.org

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

Views

Author

Peter Kagey, May 20 2025

Keywords

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

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

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

Original entry on oeis.org

1, 3, 2, 6, 13, 43, 125, 442, 1498, 5393, 19187, 69186, 248111, 888783, 3159624, 11137858, 38773614, 132891874, 446478045, 1463990116, 4662369227, 14350218212
Offset: 0

Views

Author

Peter Kagey, May 20 2025

Keywords

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.

Examples

			a(1) = 3 because the rhombicosidodecahedron is not face transitive, but has three distinct orbits of faces: (1) triangles, (2) squares, and (3) pentagons.

Links

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(21) from Bert Dobbelaere, May 26 2025

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

Original entry on oeis.org

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

Views

Author

Peter Kagey, May 20 2025

Keywords

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.

Examples

			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.

Links

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(12)-a(22) from Bert Dobbelaere, May 26 2025
Showing 1-5 of 5 results.

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