I hope you are doing well. I am working on a simple polyhedron to separate a specific cut. The polyhedron defines as P = {4x1+x2<=28, x1+4x2<=27, x1-x2<=1, x1>=0, x2>=0}. I computed the vertex and lattice points of the polyhedron by:

Code: Select all

```
$p = new Polytope(INEQUALITIES=>[[28,-4,-1],[27,-1,-4],[1,-1,1],[0,1,0],[0,0,1]]);
$p->VERTICES;
$p->LATTICE_POINTS;
```

Now, I would like to show the facets of the convex hull and also the integer convex hull. I tried:

Code: Select all

```
$p->FACETS;
```

and the results are:

Code: Select all

```
28 -4 -1
27 -1 -4
1 -1 1
0 1 0
0 0 1
```

Code: Select all

```
x1+2x2<=15
x1-x2<=1
x1<=5
x2<=6
x1>=0
x2>=0
```

My questions are:

1) What is the difference between the first generated facets and the second one? (It seems it is related to the inequalities that shape the integer convex hull).

2) How we can get the facets as same as the second set by using Polymake?

Best regards

Abbas