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A019503 Simplexity of the n-cube: minimal cardinality of triangulation of n-cube using n-simplices whose vertices are vertices of the n-cube. 8
1, 2, 5, 16, 67, 308, 1493 (list; graph; refs; listen; history; text; internal format)



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


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

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.


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.


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

Sequence in context: A124551 A005157 A019502 * A019504 A239912 A239911

Adjacent sequences:  A019500 A019501 A019502 * A019504 A019505 A019506




N. J. A. Sloane



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Last modified January 17 06:55 EST 2019. Contains 319207 sequences. (Running on oeis4.)