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 1-4 of 4 results.

A329500 Coordination sequence for 1-skeleton of truncated icosahedron or "Buckyball".

Original entry on oeis.org

1, 3, 6, 8, 10, 10, 10, 8, 3, 1
Offset: 0

Views

Author

N. J. A. Sloane, Nov 17 2019

Keywords

Comments

The truncated icosahedron is a polyhedron with 60 vertices and 32 faces. There are 20 hexagonal faces and 12 pentagonal faces. It is also known as a "Buckyball". In chemistry this structure is called a fullerene ("Buckminsterfullerene") and has formula C_60.

Crossrefs

A118785 Coordination sequence for 600-cell: number of vertices at graph distance n from a given vertex on the skeleton of the regular 600-cell (or {5,3,3}).

Original entry on oeis.org

1, 12, 32, 42, 32, 1
Offset: 0

Views

Author

Eric W. Weisstein, Apr 29 2006

Keywords

References

  • H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, page 153.

Crossrefs

A167984 Number of n-cycles on the graph of the regular 120-cell, 3 <= n <= 600.

Original entry on oeis.org

0, 0, 720, 0, 0, 3600, 2400, 4320, 28800, 35400, 64800, 284400, 540000, 1139400, 3708000, 8557200, 19677600, 55725120, 140359200, 346456800, 935942400, 2442469200, 6282571680
Offset: 3

Views

Author

Andrew Weimholt, Nov 16 2009

Keywords

Comments

The 120-cell is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol of the 120-cell is {5,3,3}.

Examples

			a(5) = 720, because there are 720 5-cycles on the graph of the 120-cell.
Cycle polynomial is 720*x^5 + 3600*x^8 + 2400*x^9 + 4320*x^10 + 28800*x^11 + 35400*x^12 + 64800*x^13 +  284400*x^14 + 540000*x^15 + 1139400*x^16 + 3708000*x^17 + 8557200*x^18 + 19677600*x^19 + 55725120*x^20 + 140359200*x^21 + 346456800*x^22 + 935942400*x^23 + ...
		

Crossrefs

Cf. A167981 (2n-cycles on graph of the tesseract).
Cf. A167982 (n-cycles on graph of 16-cell).
Cf. A167983 (n-cycles on graph of 24-cell).
Cf. A167985 (n-cycles on graph of 600-cell).
Cf. A085452 (2k-cycles on graph of n-cube).
Cf. A144151 (ignoring first three columns (0<=k<=2), k-cycles on (n-1)-simplex).
Cf. A167986 (k-cycles on graph of n-orthoplex).
Cf. A108997 (number of vertices n-steps from a given vertex on graph of 120-cell).

Extensions

a(24) from Eric W. Weisstein, Feb 21 2014
a(25) from Eric W. Weisstein, Mar 11 2014

A329499 Coordination sequence for 1-skeleton of the 24-cell (or {3,4,3}).

Original entry on oeis.org

1, 8, 14, 1
Offset: 0

Views

Author

N. J. A. Sloane, Nov 18 2019

Keywords

References

  • H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, page 149.

Crossrefs

Extensions

Name edited by Felix Fröhlich, May 14 2021
Showing 1-4 of 4 results.