© 2016 The Author(s) Shape coexistence near closed-shell nuclei, whereby states associated with deformed shapes appear at relatively low excitation energy alongside spherical ones, is indicative of the rapid change in structure that can occur with the addition or removal of a few protons or neutrons. Near68Ni (Z=28, N=40), the identification of shape coexistence hinges on hitherto undetermined transition rates to and from low-energy 0+states. In68,70Ni, new lifetimes and branching ratios have been measured. These data enable quantitative descriptions of the 0+states through the deduced transition rates and serve as sensitive probes for characterizing their nuclear wave functions. The results are compared to, and consistent with, large-scale shell-model calculations which predict shape coexistence. With the firm identification of this phenomenon near68Ni, shape coexistence is now observed in all currently accessible regions of the nuclear chart with closed proton shells and mid-shell neutrons.