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 1-3 of 3 results.

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.

Links

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

A385265 Number of edge-connected components of polygonal cells in the pinwheel tiling up to rotation of the tiling.

Original entry on oeis.org

1, 2, 4, 13, 53, 209, 904, 3963, 17900, 81745, 378554, 1768236, 8327789, 39471091, 188145066, 901117082, 4334151970, 20923370406, 101341800704, 492289834345
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

Comments

These are "one-sided" polyforms because there are no reflectional symmetries of the pinwheel tiling.
Here the "pinwheel tiling" is a tiling consisting of rectangular and square cells, and does not refer to non-periodic triangular tilings.

Links

Crossrefs

A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square), A344211 (rhombitrihexagonal), A344213 (truncated trihexagonal), A383908 (snub trihexagonal), A385266 (basketweave).

A385266 Number of edge-connected components of polygonal cells in the basketweave tiling up to rotation and reflection of the tiling.

Original entry on oeis.org

1, 2, 2, 10, 34, 166, 777, 4053, 21225, 114594, 624242, 3442399, 19121661, 106964679, 601639326, 3400619170, 19301719485, 109962791254
Offset: 0

Views

Author

Peter Kagey and Bert Dobbelaere, Jun 23 2025

Keywords

Comments

Each square cell in the basketweave tiling is edge-connected to four rectangular cells.

Links

Crossrefs

A000105 (square), A000228 (hexagonal), A000577 (triangular), A197156 (prismatic pentagonal), A197159 (floret pentagonal), A197459 (rhombille), A197462 (kisrhombille), A197465 (tetrakis square), A309159 (snub square), A343398 (trihexagonal), A343406 (truncated hexagonal), A343577 (truncated square), A344211 (rhombitrihexagonal), A344213 (truncated trihexagonal), A383908 (snub trihexagonal), A385265 (pinwheel).
Showing 1-3 of 3 results.

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

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