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 |