## General 0/1 polytopes

"Is the maximal number of facets of
0/1 polytopes bounded by an exponential function in the dimension ?"
(asked in "Recent progress on polytopes" (1996) by
Ziegler G.M.)

See U.
Kortenkamp page for the latest results on low-dimensional 0/1 polytopes
with many facets.

Here are some random polytopes with many facets (found by
T.
Christof).

(See "Efficient parallel facet
enumeration for 0/1-polytopes" (1997), Preprint, by
T.
Christof and
G.
Reinelt, Univ. of Heidelberg, for algorithmic details.)

dimension d |
# facets f |
# vertices v |
f^(1/d) |

6 |
121 |
18 |
2.22 |

7 |
432 |
30 |
2.37 |

8 |
1,675 |
38 |
2.52 |

9 |
6,875 |
48 |
2.66 |

10 |
41,591 |
83 |
2.89 |

11 |
250,279 |
106 |
3.09 |

12 |
>=1,975,935 |
152 |
3.34 |

13 |
>=17,464,356 |
254 |
3.60 |

last change: Nov 09, 1997