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 1-10 of 12 results. Next

A384068 Number of connected components of n faces of the truncated cube up to the 48 rotations and reflections of the truncated cube.

Original entry on oeis.org

1, 2, 2, 6, 14, 28, 49, 64, 68, 53, 35, 15, 7, 2, 1
Offset: 0

Views

Author

Peter Kagey, May 18 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 cube is the polyhedral dual of the triakis octahedron.

Examples

			a(1) = 2 because the truncated cube is not face-transitive but has two distinct types of faces: triangular faces and octagonal faces.
		

Crossrefs

Cf. A383800 (triakis octahedron).
Cf. A384067 (cuboctahedron), A384068 (truncated cube), A384069 (truncated octahedron), A384070 (rhombicuboctahedron), A384071 (truncated cuboctahedron), A384072 (snub cube).

A384069 Number of connected components of n faces of the truncated octahedron up to the 48 rotations and reflections of the truncated octahedron.

Original entry on oeis.org

1, 2, 2, 5, 12, 26, 52, 76, 83, 61, 39, 16, 7, 2, 1
Offset: 0

Views

Author

Peter Kagey, May 18 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 octahedron is the polyhedral dual of the tetrakis hexahedron.

Examples

			a(1) = 2 because the truncated octahedron is not face-transitive but has two distinct types of faces: square faces and hexagonal faces.
		

Crossrefs

Cf. A383802 (tetrakis hexahedron).
Cf. A384067 (cuboctahedron), A384068 (truncated cube), A384069 (truncated octahedron), A384070 (rhombicuboctahedron), A384071 (truncated cuboctahedron), A384072 (snub cube).

A384070 Number of connected components of n faces of the rhombicuboctahedron up to the 48 rotations and reflections of the rhombicuboctahedron.

Original entry on oeis.org

1, 3, 2, 6, 11, 32, 72, 207, 530, 1434, 3575, 8475, 17814, 32643, 49583, 60964, 58922, 44513, 26397, 12494, 4791, 1493, 390, 83, 17, 3, 1
Offset: 0

Views

Author

Peter Kagey, May 18 2025

Keywords

Comments

Two faces are connected if they share an edge.
These are "free" polyforms because both rotations and reflections are allowed.
The rhombicuboctahedron is the polyhedral dual of the deltoidal icositetrahedron.

Examples

			a(1) = 3 because the rhombicuboctahedron is not face-transitive but has three distinct types of faces: triangular faces, square faces that are connected to a triangular face, and square faces that are not connected to a triangular face.
		

Crossrefs

Cf. A383804 (deltoidal icositetrahedron).
Cf. A384067 (cuboctahedron), A384068 (truncated cube), A384069 (truncated octahedron), A384070 (rhombicuboctahedron), A384071 (truncated cuboctahedron), A384072 (snub cube).

Extensions

a(14)-a(26) from Bert Dobbelaere, May 22 2025

A384071 Number of connected components of n faces of the truncated cuboctahedron up to the 48 rotations and reflections of the truncated cuboctahedron.

Original entry on oeis.org

1, 3, 3, 11, 28, 100, 319, 1114, 3538, 10313, 25470, 52474, 88257, 121329, 136282, 125885, 95956, 60675, 31943, 14009, 5123, 1549, 398, 84, 17, 3, 1
Offset: 0

Views

Author

Peter Kagey, May 18 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 cuboctahedron is the polyhedral dual of the disdyakis dodecahedron.

Examples

			a(1) = 3 because the truncated cuboctahedron is not face-transitive but has three distinct types of faces: square faces, hexagonal faces, and octagonal faces.
		

Crossrefs

Cf. A383806 (disdyakis dodecahedron).
Cf. A384067 (cuboctahedron), A384068 (truncated cube), A384069 (truncated octahedron), A384070 (rhombicuboctahedron), A384071 (truncated cuboctahedron), A384072 (snub cube).

Extensions

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

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

Original entry on oeis.org

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

Views

Author

Peter Kagey, May 18 2025

Keywords

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.

Examples

			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).

Extensions

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

A384104 Number of edge-connected components of n faces of the truncated tetrahedron up to the 24 rotations and reflections of the truncated tetrahedron.

Original entry on oeis.org

1, 2, 2, 4, 7, 5, 4, 2, 1
Offset: 0

Views

Author

Peter Kagey, May 19 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 tetrahedron is the polyhedral dual of the triakis tetrahedron.

Examples

			a(1) = 2 because the truncated tetrahedron is not face-transitive but has two distinct types of faces: triangular faces and hexagonal faces.
		

Crossrefs

Cf. A383825 (triakis tetrahedron).
Cf. A384067 (cuboctahedron), A384068 (truncated cube), A384069 (truncated octahedron), A384070 (rhombicuboctahedron), A384071 (cuboctahedron), A384072 (snub cube).

Extensions

Offset corrected by Pontus von Brömssen, Jun 10 2025

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.
		

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.
		

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.
		

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.
		

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
Showing 1-10 of 12 results. Next