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 14 results. Next

A030137 Number of one-sided pentagonal n-ominoes (or pentominoes) on the dodecahedron.

Original entry on oeis.org

1, 1, 2, 5, 9, 20, 13, 12, 5, 3, 1, 1
Offset: 1

Views

Author

David W. Wilson

Keywords

Crossrefs

Cf. A030135 (free).
Cf. A030138 (icosahedron), A383491 (rhombic triacontahedron), A383493 (triakis icosahedron), A383495 (pentakis dodecahedron), A383498 (deltoidal hexecontahedron).
Cf. A197463 (kisrhombille tiling).

A383493 Number of polyforms with n cells on the faces of a triakis icosahedron up to rotation.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 15, 24, 49, 91, 182, 344, 688, 1328, 2641, 5182, 10288, 20240, 40014, 78577, 154562, 302511, 590930, 1147805, 2219309, 4260085, 8118169, 15324786, 28630807, 52826179, 96109611, 172029602, 302353990, 520508934, 875430977, 1433922264, 2279645080, 3503957379
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

These are "one-sided" polyforms.
The triakis icosahedron is the polyhedral dual of the truncated dodecahedron.

Links

Crossrefs

Cf. A383492 (free).
Cf. A030137 (dodecahedron), A030138 (icosahedron), A383491 (rhombic triacontahedron), A383495 (pentakis dodecahedron), A383497 (disdyakis triacontahedron), A383498 (deltoidal hexecontahedron).
Cf. A151531 (triakis triangular tiling).

Extensions

More terms from Bert Dobbelaere, Jun 10 2025

A383491 Number of polyforms with n cells on the faces of a rhombic triacontahedron up to rotation.

Original entry on oeis.org

1, 1, 1, 4, 6, 19, 43, 119, 300, 818, 2083, 5357, 13078
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

These are "one-sided" polyforms.
The rhombic triacontahedron is the polyhedral dual of the icosidodecahedron.

Links

Crossrefs

Cf. A383490 (free).
Cf. A030137 (dodecahedron), A030138 (icosahedron), A383493 (triakis icosahedron), A383495 (pentakis dodecahedron), A383497 (disdyakis triacontahedron), A383498 (deltoidal hexecontahedron).

A383495 Number of polyforms with n cells on the faces of a pentakis dodecahedron up to rotation.

Original entry on oeis.org

1, 1, 2, 3, 8, 18, 46, 108, 280, 694, 1788, 4544, 11740, 30105, 77584, 199102, 510910, 1305859, 3328504, 8441297, 21293077, 53315322, 132301407, 324539916, 784969397, 1866286028, 4347578908, 9887356006, 21865065180, 46806020153, 96503472390, 190548248699
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

These are "one-sided" polyforms.
The pentakis dodecahedron is the polyhedral dual of the truncated icosahedron.

Links

Crossrefs

Cf. A383494 (free).
Cf. A030137 (dodecahedron), A030138 (icosahedron), A383491 (rhombic triacontahedron), A383493 (triakis icosahedron), A383497 (disdyakis triacontahedron), A383498 (deltoidal hexecontahedron).

Extensions

a(14)-a(31) from Bert Dobbelaere, Jun 12 2025

A383498 Number of polyforms with n cells on the faces of a deltoidal hexecontahedron up to rotation.

Original entry on oeis.org

1, 1, 2, 6, 16, 48, 149, 460, 1471, 4702, 15126, 48607, 156417, 502137, 1608406, 5130178, 16278890, 51297616, 160220536, 494647640, 1504567216, 4491151455, 13098763174, 37146270208, 101880559018, 268650665645
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

These are "one-sided" polyforms.
The deltoidal hexecontahedron is the polyhedral dual of the rhombicosidodecahedron.

Links

Crossrefs

Cf. A340635 (free).
Cf. A030137 (dodecahedron), A030138 (icosahedron), A383491 (rhombic triacontahedron), A383493 (triakis icosahedron), A383495 (pentakis dodecahedron), A383497 (disdyakis triacontahedron).

Extensions

a(12)-a(25) from Bert Dobbelaere, Jun 13 2025

A383497 Number of polyforms with n cells on the faces of a disdyakis triacontahedron up to rotation.

Original entry on oeis.org

1, 2, 3, 6, 13, 28, 66, 148, 349, 828, 2004, 4860, 11919, 29280, 72348, 179062, 444357, 1104030, 2747476, 6843910, 17067229, 42593112, 106362575, 265693836, 663811498, 1658352602, 4141998151, 10341234170, 25805349073, 64352577616
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

These are "one-sided" polyforms.
The disdyakis triacontahedron is the polyhedral dual of the truncated icosidodecahedron.

Links

Crossrefs

Cf. A383496 (free).
Cf. A030137 (dodecahedron), A030138 (icosahedron), A383491 (rhombic triacontahedron), A383493 (triakis icosahedron), A383495 (pentakis dodecahedron), A383498 (deltoidal hexecontahedron).
Cf. A197463 (kisrhombille tiling).

Extensions

a(1) corrected and a(13)-a(29) from Bert Dobbelaere, Jun 13 2025

A340635 Number of free deltoidal hexecontahedron polykites with n faces.

Original entry on oeis.org

1, 2, 4, 10, 27, 80, 238, 751, 2374, 7608, 24371, 78341, 251269, 804594, 2565683, 8140581, 25650546, 80113477, 247328763, 752292342, 2245589193, 6549404314, 18573169874, 50940335705, 134325417269
Offset: 1

Views

Author

Hilarie Orman, Jan 14 2021

Keywords

Comments

The surface of a deltoidal hexecontahedron has 60 congruent faces. Edge-connected faces are called polykites. Reflections are included separately in the counts. Polykites can have from 1 to 60 faces.
These polykites are counted up to the full icosahedral group (order 120) of the deltoidal hexecontahedron. - Peter Kagey, Apr 28 2025

Links

Crossrefs

Cf. A057786.
Cf. A030137 (dodecahedron), A030138 (icosahedron).

Extensions

a(13)-a(25) from Bert Dobbelaere, Jun 13 2025

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.

A383786 Number of polyforms with n cells on the faces of a pentagonal hexecontahedron up to rotation.

Original entry on oeis.org

1, 1, 3, 8, 25, 80, 281, 967, 3451, 12256, 43924, 157090
Offset: 0

Views

Author

Peter Kagey, May 09 2025

Keywords

Links

Crossrefs

Cf. A030137 (dodecahedron), A030138 (icosahedron), A383491 (rhombic triacontahedron), A383493 (triakis icosahedron), A383495 (pentakis dodecahedron), A383498 (deltoidal hexecontahedron).
Cf. A197159 (floret pentagonal).

A383801 Number of polyforms with n cells on the faces of a triakis octahedron up to rotation.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 15, 24, 48, 81, 149, 255, 458, 730, 1148, 1623, 2112, 2325, 2075, 1175, 410, 84, 16, 1, 1
Offset: 0

Views

Author

Peter Kagey, May 10 2025

Keywords

Comments

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

Links

Crossrefs

Cf. A383800 (free).
Tetrahedral symmetry: A383826.
Octahedral symmetry: A383799 (row 3), A383801, A383803, A383805, A383807, A383808.
Icosahedral symmetry: A030137, A030138, A383491, A383493, A383495, A383497, A383498, A383786.
Showing 1-10 of 14 results. Next

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