A019502 Number of simplices in minimal decomposition of an n-cube.

1, 2, 5, 16, 67

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• hard
• nice
• more

References

• H. T. Croft, K. J. Falconer and R. K. Guy, Unsolved Problems in Geometry, Section C9.
• R. K. Guy, What is the simplexity of the d-cube?, Amer. Math. Monthly, 91:10 (1984), 628-629.

Links

• A. Bliss, F. E. Su, Lower bounds for simplicial covers and triangulations of cubes, arXiv:math/0310142 [math.CO], 2003 (see Table 1 page 4).
• A. Bliss, F. E. Su. Lower bounds for simplicial covers and triangulations of cubes, Discrete Comput. Geom. 33 (2005), 669-686.
• R. B. Hughes and M. R. Anderson, Simplexity of the cube, Discrete Math., 158(1-3):99-150, 1996.
• John F. Sallee, A note on minimal triangulations of an n-cube, Discrete Appl. Math. 4 (1982), no. 3, 211--215. MR0675850 (84g:52019).
• John F. Sallee, The middle-cut triangulations of the n-cube, SIAM J. Algebraic Discrete Methods 5 (1984), no. 3, 407--419. MR0752044 (86c:05054). See Table 2.
• John F. Sallee, A triangulation of the n-cube, Discrete Math. 40 (1982), no. 1, 81--86. MR0676714 (84d:05065b).

Crossrefs

Other sequences dealing with different ways to attack this problem. They give further references: A019503, A019504, A166932, A166932, A239912, A275518.

See also A094294, A238820, A238821.