A105231 Number of n-dimensional polytopes with vertices from {0,1}^n up to (0,1)-equivalence.

1, 2, 12, 347, 1226525, 400507800465455

Offset: 1

Author

N. J. A. Sloane, Apr 16 2005

Keywords

• nonn
• hard
• more

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, Birkhäuser, 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

Cf. A105230, A105232.

Extensions

a(6) from Andrey Zabolotskiy, Jun 20 2023