# Can the base ring of a polyhedron be restricted?

I have a polyhedron `P`

with rational vertices

```
sage: A = matrix([[1,0,0],[1,0,2],[1,1,1],[1,3/2,0]])
sage: A
[ 1 0 0]
[ 1 0 2]
[ 1 1 1]
[ 1 3/2 0]
sage: P = Polyhedron(A)
sage: P
A 2-dimensional polyhedron in QQ^3 defined as the convex hull of 4 vertices
```

If we scale `P`

by a factor of two, then we get a lattice polytope.

```
sage: (2*P).is_lattice_polytope()
True
```

However, the base ring of `P`

is still `QQ`

```
sage: (2*P).parent()
Polyhedra in QQ^3
```

Since `2*P`

is a lattice polytope it seems like it should be possible to restrict the base ring of `2*P`

to `ZZ`

. Is this possible?