# Use solve with inequality extracted from polytope

Starting from a polytope, I would like to extract the inequalities
of its hyperplane representation and solve them with Sage's `solve`

.

Define the dodecahedron and obtain its hyperplane representation.

```
sage: D = polytopes.dodecahedron()
sage: DH = D.Hrepresentation()
```

Pick the first inequality:

```
sage: DH[0]
An inequality (0, -1/2, -1/4*sqrt5 - 1/4) x + 1 >= 0
```

Try to feed it to `solve`

:

```
sage: sol = solve(DH[0], x[1])
```

This doesn't work. So what can I do?

Could you please provide the constructions of all objects so that we could reproduce ?

Sorry for my distraction the polyhedron was not in the cell. I have corrected my question.

What do you want to achieve at the end ? Even if you could transform this inequality into a symbolic inequality, there will be infinitely many solutions (a whole half-space).

It's to demonstrate step by step Fourier -Motzkin elimination. I have done it with your help for one variable. I want to be able to do it as I do it on a sheet of paper. I want after to plot the 3 D polyhedra then its projections in 2D abd then in 2D.

Instead of "this doesn't work", say what error you get, and what you were hoping to get.