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 15 results. Next

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).

A383492 Number of polyforms with n cells on the faces of a triakis icosahedron up to rotation and reflection.

Original entry on oeis.org

1, 1, 2, 2, 4, 4, 10, 13, 29, 47, 99, 175, 358, 669, 1346, 2600, 5191, 10137, 20093, 39320, 77437, 151314, 295745, 574011, 1110144, 2130239, 4059919, 7662738, 14316799, 26413683, 48057066, 86015788, 151180505, 260256043, 437720722, 716963561, 1139830037, 1751982279, 2592522277
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

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

Links

Crossrefs

Cf. A383493 (one-sided).
Cf. A030135 (dodecahedron), A030136 (icosahedron), A340635 (deltoidal hexecontahedron), A383490 (rhombic triacontahedron), A383494 (pentakis dodecahedron), A383496 (disdyakis triacontahedron).
Cf. A057784 (triakis triangular tiling).

Extensions

More terms from Bert Dobbelaere, Jun 10 2025

A383496 Number of polyforms with n cells on the faces of a disdyakis triacontahedron up to rotation and reflection.

Original entry on oeis.org

1, 1, 3, 3, 9, 14, 38, 74, 185, 414, 1025, 2430, 6012, 14640, 36294, 89531, 222452, 552015, 1374367, 3421955, 8535077, 21296556, 53184718, 132846918, 331913842, 829176301, 2071018243, 5170617085, 12902719975, 32176288808
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

These are "free" polyforms.
The disdyakis triacontahedron is the polyhedral dual of the truncated icosidodecahedron.

Links

Crossrefs

Cf. A383497 (one-sided).
Cf. A030135 (dodecahedron), A030136 (icosahedron), A340635 (deltoidal hexecontahedron), A383490 (rhombic triacontahedron), A383492 (triakis icosahedron), A383494 (pentakis dodecahedron).
Cf. A197462 (kisrhombille tiling).

Extensions

a(14)-a(29) from Bert Dobbelaere, Jun 13 2025

A383494 Number of polyforms with n cells on the faces of a pentakis dodecahedron up to rotation and reflection.

Original entry on oeis.org

1, 1, 2, 2, 6, 10, 27, 56, 149, 352, 915, 2285, 5919, 15084, 38908, 99627, 255728, 653113, 1664892, 4221090, 10648018, 26658710, 66154031, 162272380, 392491903, 933148405, 2173804324, 4943689469, 10932561700, 23403033225, 48251790080, 95274168428
Offset: 0

Views

Author

Peter Kagey, Apr 28 2025

Keywords

Comments

These are "free" polyforms.
The pentakis dodecahedron is the polyhedral dual of the truncated icosahedron.

Links

Crossrefs

Cf. A383495 (one-sided).
Cf. A030135 (dodecahedron), A030136 (icosahedron), A340635 (deltoidal hexecontahedron), A383490 (rhombic triacontahedron), A383492 (triakis icosahedron), A383496 (disdyakis triacontahedron).

Extensions

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

A383802 Number of polyforms with n cells on the faces of a tetrakis hexahedron up to rotation and reflection.

Original entry on oeis.org

1, 1, 2, 2, 6, 8, 21, 36, 84, 164, 356, 691, 1361, 2342, 3707, 4830, 5082, 3843, 2128, 798, 248, 50, 12, 1, 1
Offset: 0

Views

Author

Peter Kagey, May 10 2025

Keywords

Comments

These are "free" polyforms.
The tetrakis hexahedron is the polyhedral dual of the truncated octahedron.

Links

Crossrefs

Cf. A383803 (one-sided).
Octahedral symmetry: A333333 (row 3), A383800, A383802, A383804, A383806.
Icosahedral symmetry: A030135, A030136, A340635, A383490, A383492, A383494, A383496.
Cf. A197465 (tetrakis square tiling).

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

A383974 Number of connected subsets of n edges of the icosahedron up to the 120 rotations and reflections of the icosahedron.

Original entry on oeis.org

1, 1, 2, 8, 27, 126, 557, 2503, 10270, 37542, 114926, 283958, 552542, 866843, 1129291, 1250835, 1195298, 993613, 720889, 456329, 251444, 119989, 49269, 17238, 5113, 1257, 262, 46, 8, 1, 1
Offset: 0

Views

Author

Peter Kagey, May 16 2025

Keywords

Comments

Connected subsets of edges are also called "polysticks," "polyedges," and "polyforms."
These are "free" polyforms, in that two polyforms are equivalent if one can be mapped to the other using the 120 symmetries of the icosahedron.

Links

Crossrefs

Cf. A333333 (cube, row 3), A383490 (dodecahedron), A383973 (octahedron, row 3), A383975 (tetrahedron, row 3).

Extensions

a(11)-a(30) from Bert Dobbelaere, May 25 2025

A383981 Number of connected subsets of n edges of the rhombic dodecahedron up to the 48 rotations and reflections of the rhombic dodecahedron.

Original entry on oeis.org

1, 1, 3, 5, 16, 39, 127, 357, 1067, 2861, 7071, 14827, 25638, 33730, 33189, 24838, 14954, 7188, 2905, 912, 254, 49, 11, 1, 1
Offset: 0

Views

Author

Peter Kagey, May 16 2025

Keywords

Comments

Connected subsets of edges are also called "polysticks," "polyedges," and "polyforms."
These are "free" polyforms, in that two polyforms are equivalent if one can be mapped to the other using the 48 symmetries of the rhombic dodecahedron.

Crossrefs

Cf. A019988.
Cf. A333333 (cube, row 3), A383490 (dodecahedron), A383973 (octahedron, row 3), A383974 (icosahedron), A383974 (tetrahedron, row 3), A383981 (rhombic dodecahedron), A383982 (cuboctahedron), A383983 (rhombic triacontahedron), A383984 (icosidodecahedron).
Showing 1-10 of 15 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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