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 1-7 of 7 results.

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.

Links

Crossrefs

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

A383803 Number of polyforms with n cells on the faces of a tetrakis hexahedron up to rotation.

Original entry on oeis.org

1, 1, 2, 3, 8, 14, 35, 68, 154, 318, 683, 1362, 2668, 4645, 7326, 9594, 10048, 7605, 4145, 1539, 445, 86, 16, 1, 1
Offset: 0

Views

Author

Peter Kagey, May 10 2025

Keywords

Comments

These are "one-sided" polyforms.
The tetrakis hexahedron is the polyhedral dual of the truncated octahedron.

Links

Crossrefs

Cf. A383802 (free), A383827.
Tetrahedral symmetry: A383826.
Octahedral symmetry: A383799 (row 3), A383801, A383803, A383805, A383807, A383808.
Icosahedral symmetry: A030137, A030138, A383491, A383493, A383495, A383497, A383498, A383786.

A383800 Number of polyforms with n cells on the faces of a triakis octahedron up to rotation and reflection.

Original entry on oeis.org

1, 1, 2, 2, 4, 4, 10, 13, 28, 42, 81, 130, 239, 369, 587, 817, 1072, 1170, 1054, 594, 217, 46, 11, 1, 1
Offset: 0

Views

Author

Peter Kagey, May 10 2025

Keywords

Comments

These are "free" polyforms.
The triakis octahedron is the polyhedral dual of the truncated cube.

Links

Crossrefs

Cf. A383801 (one-sided).
Octahedral symmetry: A333333 (row 3), A383800, A383802, A383804, A383806.
Icosahedral symmetry: A030135, A030136, A340635, A383490, A383492, A383494, A383496.

A383804 Number of polyforms with n cells on the faces of a deltoidal icositetrahedron up to rotation and reflection.

Original entry on oeis.org

1, 1, 2, 4, 10, 23, 65, 166, 453, 1157, 2849, 6252, 11894, 18183, 21614, 19139, 12966, 6691, 2813, 901, 253, 49, 11, 1, 1
Offset: 0

Views

Author

Peter Kagey, May 10 2025

Keywords

Comments

These are "free" polyforms.
The deltoidal icositetrahedron is the polyhedral dual of the rhombicuboctahedron.

Links

Crossrefs

Cf. A383805 (one-sided).
Octahedral symmetry: A333333 (row 3), A383800, A383802, A383804, A383806.
Icosahedral symmetry: A030135, A030136, A340635, A383490, A383492, A383494, A383496.

A383806 Number of polyforms with n cells on the faces of a disdyakis dodecahedron up to rotation and reflection.

Original entry on oeis.org

1, 1, 3, 3, 9, 14, 38, 74, 184, 406, 981, 2262, 5398, 12589, 29700, 69289, 161727, 373879, 858884, 1948493, 4358729, 9560977, 20489431, 42663444, 85863997, 165915428, 305531365, 531313203, 863339197, 1294513104, 1765472012, 2153407639, 2304457468, 2119172241, 1641722694
Offset: 0

Views

Author

Peter Kagey, May 10 2025

Keywords

Comments

These are "free" polyforms.
The disdyakis dodecahedron is the polyhedral dual of the truncated cuboctahedron.

Links

Crossrefs

Cf. A383807 (one-sided).
Octahedral symmetry: A333333 (row 3), A383800, A383802, A383804, A383806.
Icosahedral symmetry: A030135, A030136, A340635, A383490, A383492, A383494, A383496.

Extensions

More terms from Bert Dobbelaere, Jun 08 2025

A383825 Number of polyforms with n cells on the faces of a triakis tetrahedron up to rotation and reflection.

Original entry on oeis.org

1, 1, 2, 2, 4, 4, 9, 9, 14, 10, 5, 1, 1
Offset: 0

Views

Author

Peter Kagey, May 11 2025

Keywords

Comments

These are "free" polyforms.
The triakis tetrahedron is the polyhedral dual of the truncated tetrahedron.

Links

Crossrefs

Cf. A383826 (one-sided).
Octahedral symmetry: A333333 (row 3), A383800, A383802, A383804, A383806.
Icosahedral symmetry: A030135, A030136, A340635, A383490, A383492, A383494, A383496.

A383827 Number of polyforms with n cells on the faces of a tetrakis hexahedron up to tetrahedral symmetry.

Original entry on oeis.org

1, 1, 3, 3, 9, 14, 37, 68, 156, 318, 685, 1362, 2664, 4645, 7306, 9594, 10016, 7605, 4130, 1539, 444, 86, 16, 1, 1
Offset: 0

Views

Author

Peter Kagey, May 11 2025

Keywords

Comments

The triangular faces of the tetrakis hexahedron represent the 24 fundamental domains of tetrahedral symmetry.
The tetrakis hexahedron is the polyhedral dual of the truncated octahedron.

Links

Crossrefs

Cf. A383802, A383803.
Showing 1-7 of 7 results.

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