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A167982 Number of n-cycles on the graph of the regular 16-cell, 3 <= n <= 8. 4
32, 102, 288, 640, 960, 744 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

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}.

LINKS

Table of n, a(n) for n=3..8.

A. Weimholt, 16-cell net

Eric Weisstein's World of Mathematics, 16-Cell

Eric Weisstein's World of Mathematics, Cycle Polynomial

EXAMPLE

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.

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).

Sequence in context: A172517 A194645 A134845 * A063498 A173951 A233691

Adjacent sequences:  A167979 A167980 A167981 * A167983 A167984 A167985

KEYWORD

fini,full,nonn

AUTHOR

Andrew Weimholt, Nov 16 2009

STATUS

approved

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Last modified January 28 13:34 EST 2022. Contains 350656 sequences. (Running on oeis4.)