  We report self-consistent calculations of the gap symmetry for the iron-based
high-temperature superconductors using realistic small-q phonon mediated
pairing potentials and four-band energy dispersions. When both electron and
hole Fermi surface pockets are present, we obtain the nodeless $s_\pm$ state
that was first encountered in a spin-fluctuations mechanism picture. Nodal gap
structures such as $d_{x^2-y^2}$ and $s_\pm+d_{x^2-y^2}$ and even a p-wave
triplet state, are accessible upon doping within our phononic mechanism. Our
results resolve the conflict between phase sensitive experiments reporting a
gap changing sign attributed previously only to a non-phononic mechanism and
isotope effect measurements proving the involvement of phonons in the pairing.
