# Hasse diagram of different dimensional cells of a polyhedron

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

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

For instance, I have:

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

I don't know how to extract this kind of information from this.

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

Not clear to me what more you would like to have. E is exactly what you want, except for the added empty face of dimension -1. You can see the Hasse diagram using

`E.plot(label_elements=False)`

.