### Hasse diagram of different dimensional cells of a polyhedron

I am trying to get a facet poset diagram of a ~~polyhedron. ~~polyhedron.
What I want is an adjacency matrix describing the Hasse ~~diagram/poset ~~diagram/poset
where vertices are cells, and two vertices are connected by an ~~edge ~~edge
if one of their corresponding cells is contained in the ~~other.
~~other.

So I want a Hasse diagram where the top row consists of a ~~vertex ~~vertex
for the highest dimensional cell, then the next row consists ~~of ~~of
cells of one less dimension, and so on until the final ~~row ~~row
corresponding to vertices.

For instance, I have:

```
E = polytopes.dodecahedron().face_lattice()
```

~~E=polytopes.dodecahedron().face_lattice()
~~I don't know how to extract this kind of information from ~~this.
~~this.

I want to be able to plot the cell poset diagram in some other software to look at it.