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A019503 Minimal cardinality of triangulation of n-cube using n-simplices whose vertices are vertices of the n-cube. 3
1, 2, 5, 16, 67, 308, 1493 (list; graph; refs; listen; history; internal format)
OFFSET

1,2

REFERENCES

H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, C9.

R. B. Hughes and M. R. Anderson, Simplexity of the cube, Discrete Mathematics, 158 (1996) 99-150, esp. p. 100.

Mark Haiman, "A simple and relatively efficient triangulation of the n-cube", Discrete Comput. Geometry 6 (1991), 287-289.

Warren D. Smith, "Lower bounds for triangulations of the N-cube," 1994.

Gunter M. Ziegler, Lectures on Polytopes, Revised First Edn., Graduate Texts in Mathematics, Springer, 1994, p. 147.

C. Zong, What is known about unit cubes, Bull. Amer. Math. Soc., 42 (2005), 181-211.

FORMULA

5522 <= a(8) <= 11944 [Haiman, Ziegler]. For large n, a method due to Smith, using volume estimates in hyperbolic geometry, yields the best lower bounds on a(n) so far. - Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 13 2005

CROSSREFS

Cf. A019502, A019504.

Sequence in context: A124551 A005157 A019502 * A019504 A005163 A006116

Adjacent sequences:  A019500 A019501 A019502 * A019504 A019505 A019506

KEYWORD

nonn,hard,nice,more

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified February 17 15:44 EST 2012. Contains 206050 sequences.