A167982 Number of n-cycles on the graph of the regular 16-cell, 3 <= n <= 8.

32, 102, 288, 640, 960, 744

Offset: 3

Author

Andrew Weimholt, Nov 16 2009

Keywords

• fini
• full
• nonn

Comments

Row n=3 of the triangle in A167986

The 16-cell is the dual polytope of the tesseract, and is one of 6 regular convex polytopes in 4 dimensions. The Schläfli symbol for the 16-cell is {3,3,4}.

Examples

			a(3) = 32, because there are 32 3-cycles on the graph of the 16-cell.
Cycle polynomial is 32*x^3 + 102*x^4 + 288*x^5 + 640*x^6 + 960*x^7 + 744*x^8.
		

Links

• A. Weimholt, 16-cell net
• Eric Weisstein's World of Mathematics, 16-Cell
• Eric Weisstein's World of Mathematics, Cycle Polynomial

Crossrefs

Cf. A167981 (2n-cycles on graph of the tesseract).

Cf. A167983 (n-cycles on graph of 24-cell).

Cf. A167984 (n-cycles on graph of 120-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).