## Maximal number of (in)equalities allowed for polytope.

General discussion on polymake goes here.
AlexiosFanus
Posts: 2
Joined: 13 Jun 2024, 20:14

### Maximal number of (in)equalities allowed for polytope.

Hi,
I am using polytope for the computation of a polytope with factorially many vertices. This definitely requires many computation resources, so I wonder what is the capacity of polytope. In my case, the process is killed if I run the software with 10! vertices, while 9! vertices can be computed in some cases. Is this related to the memory of the computer? I am running on a 16GB RAM, would upgrading to 32GB enable more computation power?

joswig
Main Author
Posts: 288
Joined: 24 Dec 2010, 11:10

### Re: Maximal number of (in)equalities allowed for polytope.

It is not easy or next to impossible to predict the amount of resources required for a convex hull computation a priori. There is only McMullen's upper bound theorem, which gives some guidance.

For instance, this is the maximal number of facets of a polytope in dimension 10 with 10! vertices.

Code: Select all

polytope > print upper_bound_theorem(10,fac(10))->F_VECTOR->[9]; 5243609334812596924626062645760 
If you should be near that bound, then there is not enough RAM to buy for the convex hull computation.

Of course, your examples may be much smaller. But there is nothing else but trying it out.

AlexiosFanus
Posts: 2
Joined: 13 Jun 2024, 20:14

### Re: Maximal number of (in)equalities allowed for polytope.

Hey, thanks for the reply! I think the polytope I am looking for does not have that many facets, but a rather small amount, say a thousand to five thousand. Would this imply that RAM-upgrade is a potential solution?