

A019503


Simplexity of the ncube: minimal cardinality of triangulation of ncube using nsimplices whose vertices are vertices of the ncube.


8




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.
Warren D. Smith, Lower bounds for triangulations of the Ncube, 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 ncube, Discrete Math. 312 (2012), no. 24, 36563662. MR2979495.  From N. J. A. Sloane, Nov 07 2012
R. B. Hughes and M. R. Anderson, Simplexity of the cube, Discrete Mathematics, 158 (1996) 99150, esp. p. 100.
Mark Haiman, A simple and relatively efficient triangulation of the ncube, Discrete Comput. Geometry 6 (1991), 287289.
D. Orden, F. Santos, Asymptotically efficient triangulations of the dcube, Discr. Comput. Geom. 30 (2003) 509, Table 1.
Warren D. Smith, A lower bound for the simplexity of the ncube via hyperbolic volumes, Combinatorics of polytopes. European J. Combin. 21 (2000), no. 1, 131137. MR1737333 (2001c:52004).
Chuanming Zong, What is known about unit cubes, Bull. Amer. Math. Soc., 42 (2005), 181211.


CROSSREFS

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


KEYWORD

nonn,hard,nice,more


AUTHOR

N. J. A. Sloane


STATUS

approved



