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

1200, 5400, 29520, 187200, 1310400, 9813600, 77193600, 630538632, 5307656400

Offset

3,1

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}.

Links

Table of n, a(n) for n=3..11.

A. Weimholt, 600-cell net

Eric Weisstein's World of Mathematics, 600-Cell

Eric Weisstein's World of Mathematics, Cycle Polynomial

Example

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).

Sequence in context: A252531 A043408 A234917 * A237001 A022056 A107520

Adjacent sequences: A167982 A167983 A167984 * A167986 A167987 A167988

Keyword

fini,more,nonn,hard

Author

Andrew Weimholt, Nov 16 2009

Extensions

a(11) from Eric W. Weisstein, Feb 09 2014

Status

approved