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

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice
• more

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

• A. Glazyrin, Lower bounds for the simplexity of the n-cube, Discrete Math. 312 (2012), no. 24, 3656--3662. MR2979495. - _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 and 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.