Hello,

Given a polyhedron you can obtain their faces with the method faces. Then you can convert them to polyhedra and intersect them. In action

```
sage: P1 = Polyhedron([(0,0),(1,2),(3,4)])
sage: P2 = Polyhedron([(0,0),(1,2),(-3,-2)])
sage: f1 = [f.as_polyhedron() for f in P1.faces(1)]
sage: f2 = [f.as_polyhedron() for f in P2.faces(1)]
```

f1 is just the faces of my first polyhedron (seen themselves as polyhedra)

```
sage: f1[0].vertices_list()
[[0, 0], [1, 2]]
sage: f1[1].vertices_list()
[[0, 0], [3, 4]]
sage: f1[2].vertices_list()
[[1, 2], [3, 4]]
```

idem for f2

```
sage: f2[0].vertices_list()
[[-3, -2], [0, 0]]
sage: f2[1].vertices_list()
[[-3, -2], [1, 2]]
sage: f2[2].vertices_list()
[[0, 0], [1, 2]]
```

And you can now do intersection between them

```
sage: f1[0].intersection(f2[0])
A 0-dimensional polyhedron in ZZ^2 defined as the convex hull of 1 vertex
sage: f1[0].intersection(f2[2])
A 1-dimensional polyhedron in ZZ^2 defined as the convex hull of 2 vertices
```

Then, for plotting a polyhedra **P** just do **P.plot()** or **P.show()**. To see the options you have for plotting, you can have a look at the documentation obtained by typing enter after **P.plot?** or **P.show?** (with the question mark). There is also the possibility to make a tikz picture if you are interested.

Vincent