OFFSET

1,2

COMMENTS

a(6) = 400507800465455 is obtained as the sum of the number of 6-dimensional polytopes with up to 12 vertices, 94826705, given in the footnote in p. 119 of Aichholzer (2000), and the counts for k > 12 vertices F_6(k) given in tables 3, 6 and 7 of Chen & Guo (2014). Chen & Guo have typos: F_5(29) in table 2 should be 10 and F_5(16) in table 5 should be 169110 (cf. polyDB or Aichholzer's table 2). - Andrey Zabolotskiy, Jun 20 2023

LINKS

Oswin Aichholzer, Extremal Properties of 0/1-Polytopes of Dimension 5. In: Polytopes - Combinatorics and Computation, DMV Seminar vol 29, BirkhĂ¤user, Basel, 2000.

William Y. C. Chen and Peter L. Guo, Equivalence Classes of Full-Dimensional 0/1-Polytopes with Many Vertices, Discrete Comput. Geom., 52 (2014), 630-662.

Andreas Paffenholz and the polymake team, polyDB. See Polytopes > Geometric Polytopes > 0/1 Polytopes by Oswin Aichholzer.

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

CROSSREFS

KEYWORD

nonn,hard,more

AUTHOR

N. J. A. Sloane, Apr 16 2005

EXTENSIONS

a(6) from Andrey Zabolotskiy, Jun 20 2023

STATUS

approved