# Polyhedra, facets and vertices

I have a 6-dimensional, convex, compact polyhedron in $\mathbb{R}^{12}$, that I am calling `P1`

.
The polyhedron `P1`

was specified by giving a large number of inequalities.
When I enter `P1.faces(5)`

into Sage, I get the following

```
(A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 6 vertices,
A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 7 vertices,
A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 7 vertices,
A 6-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 7 vertices,
A 5-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 6 vertices,
A 6-dimensional face of a Polyhedron in RDF^12 defined as the convex hull of 8 vertices,
...)
```

How can there be two 6-dimensional faces, each with a different number of vertices,
on the boundary of `P1`

? I have checked that `P1`

really does have dimension 6.

Also, when I try to find a list of vertices on the boundary of any 5-dimensional face of `P1`

,
for example

```
P1.faces(5)[0].vertices_list()
```

I get an error message

```
AttributeError: 'tuple' object has no attribute 'vertices_list'
```

However, `P1.faces(5)[0].vertices()`

works.

My second question is, how do I get a list of vertices on the boundary of an $n$-dimensional face?