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

A108997 Coordination sequence for the 120-cell: number of vertices n steps away from a given vertex on the regular 120-cell (hecatonicosachoron or {3,3,5}).

Original entry on oeis.org

1, 4, 12, 24, 36, 52, 68, 76, 78, 72, 64, 56, 40, 12, 4, 1
Offset: 0

Views

Author

Andrew Weimholt, Jul 29 2005

Keywords

Comments

The adjacency graph of the 120-cell is a 4-regular graph of girth 5 (pentagonal cycles) and diameter 15. There are 30 distinct nonzero distances between vertices of the 120-cell in 4-space. - Michael Somos, Aug 09 2005

References

  • H. S. M. Coxeter, Introduction to geometry. 2nd edition, John Wiley & Sons, Inc., 1969, pp. 153, 404. MR0346644 (49 #11369)

Crossrefs

A167985 Number of n-cycles on the graph of the regular 600-cell, 3 <= n <= 120.

Original entry on oeis.org

1200, 5400, 29520, 187200, 1310400, 9813600, 77193600, 630538632, 5307656400
Offset: 3

Views

Author

Andrew Weimholt, Nov 16 2009

Keywords

Comments

The 600-cell is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol for the 600-cell is {3,3,5}.

Examples

			a(3) = 1200, because there are 1200 3-cycles on the graph of the 600-cell.
Cycle polynomial is 1200*x^3 + 5400*x^4 + 29520*x^5 + 187200*x^6 + 1310400*x^7 + 9813600*x^8 + 77193600*x^9 + 630538632*x^10 + ...
		

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. A167984 (n-cycles on graph of 120-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. A118785 (number of vertices n-steps from a given vertex on graph of the 600-cell).

Extensions

a(11) from Eric W. Weisstein, Feb 09 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.