1 | | Given an (abstract) `CombinatorialPolyhedron` such that **at least one** of H-representation and V-representation are labeled geometrically, we should be able to efficiently build a polyhedron -- or raise an error if the data are inconsistent. |

| 1 | Given an (abstract) `CombinatorialPolyhedron` such that **at least one** of H-representation and V-representation are labeled geometrically, the new method `CombinatorialPolyhedron.as_polyhedron` constructs a geometric polyhedron. |

| 2 | |

| 3 | If `check=True` (default), it checks that the result is OK. |

| 4 | |

| 5 | We should be able to efficiently build a polyhedron, avoiding to run the double description method when setting up the polyhedron, for the backends that accept double description input: |

| 6 | - if both representations are geometric, just pass them to the polyhedron constructor (#26366) |

| 7 | - if only one representation is geometric, reconstruct the other one from the incidences by equation solving. |