def pair_hf_to_uv(volmesh, network):
    """Pairs the directed halffaces of a volmesh to the corresponding edge (u, v) of the dual network.

    Parameters
    ----------
    volmesh : VolMesh
        A volmesh object representing a polyhedral force diagram.
    network : Network
        A network object representing a polyhedral form diagram.

    Returns
    -------
    dictionary
        A dictionary of u_hfkey-(u, v) pairs.

    Notes
    -----
    u_hfkey is an interior halfface of the volmesh that belongs to volmesh.cell[u], which points to volmesh.cell[v]. In another words, its pair (or opposite) halfface belongs to volmesh.cell[v].

    """
    hf_uv_dict = {}
    for u, v in network.edges():
        u_hfkey, v_hfkey = volmesh.cell_pair_halffaces(u, v)
        hf_uv_dict[u_hfkey] = u, v
        hf_uv_dict[v_hfkey] = v, u
    return hf_uv_dict
