A019503 Simplexity of the n-cube: minimal cardinality of triangulation of n-cube using n-simplices whose vertices are vertices of the n-cube.

1, 2, 5, 16, 67, 308, 1493

Offset

1,2

Comments

5522 <= a(8) <= 11944 [Haiman, Ziegler]. - Jonathan Vos Post, Jul 13 2005

References

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

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 8.9, p. 512.

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

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

Links

Table of n, a(n) for n=1..7.

A. Glazyrin, Lower bounds for the simplexity of the n-cube, Discrete Math. 312 (2012), no. 24, 3656--3662. MR2979495. - From N. J. A. Sloane, Nov 07 2012

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.

D. Orden, F. Santos, Asymptotically efficient triangulations of the d-cube, Discr. Comput. Geom. 30 (2003) 509, Table 1.

Warren D. Smith, A lower bound for the simplexity of the n-cube via hyperbolic volumes, Combinatorics of polytopes. European J. Combin. 21 (2000), no. 1, 131-137. MR1737333 (2001c:52004).

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

Crossrefs

Other sequences dealing with different ways to attack this problem. They give further references: A019502, A019504, A166932, A166932, A239912, A275518.

Sequence in context: A005157 A340021 A019502 * A019504 A239912 A239911

Adjacent sequences: A019500 A019501 A019502 * A019504 A019505 A019506

Keyword

nonn,hard,nice,more

Author

N. J. A. Sloane

Status

approved