The role of structure in the nonmetal-metal transition of Co clusters is investigated by performing calculations for different symmetries: hexahedral, octahedral and decahedral. This transition occurs when the density of states at the Fermi level exceeds 1/kT and the discrete energy levels begin to form a quasi-continuous band. The electronic structure is calculated including spd orbitals and spillover effects in a Hubbard Hamiltonian solved within the unrestricted Hartree-Fock approximation. We find that in small clusters (N < 40) the metallic behavior is strongly related to the geometrical structure of the cluster. We compare our results with those coming out of a simple Friedel's model.