Below Pb (Z=82), two distinct shapes can be seen in the
Pt (Z=78) and Hg (Z=80) isotopes.
This is shown below, where the solid circles represent excitation energies for the near-spherical structure, while the open circles represent deformed structure.

The Pt isotopes have a small oblate deformation in their ground states, then quite suddenly become very prolate deformed. This is in agreement with experimental observations, where the deformed structure becomes the ground state at N=108.
The Hg isotopes have a predicted small oblate deformation across a wide range of neutron numbers; again, this is observed experimentally as the deformed structure never becomes the ground state for these isotopes.

So what is causing this deformed structure? It is thought that the excitation of two protons across the Z=82 shell gap is responsible for the shape coexistence. There are many papers discussing this for the Pt and Hg nuclei. A couple of good references are:

So what happens above Z=82? The FRDM calculations suggest shape coexstence effects similar to what is observed below Z=82. However, the experimental data is less convincing.
Shown below are the experimental excitations for the even-even Po, Rn, and Ra isotopes (Z=84, 86, 88, respectively). As before, dark circles represent proposed spherical (or near-spherical) structures, while open circles suggest deformed structure.

A large amount of work, both experimental and theoretical, has been done on the Po isotopes. The FRDM calculations suggest that the Po isotopes are nearly-=spherical in their ground states until N=110, where they become oblate deformed. By N=106, they are strongly prolate-deformed. The intruder structure has been argued to be the sought-after deformed structure, or a vibrational structure. Lifetimes of the excited states will need to be performed to determine the relative deformation of the secondary structure. By coupling the Yale plunger (NYPD) to SASSYER, perhaps lifetimes of these important states may be elucidated.

The oblate intruder structure in the Rn isotopes is predicted to occur much earlier, at approximately N=116. Experimentally, the secondary structure is less defined. These excited states are populated relatively weakly in typical heavy-ion fusion evaporation reactions, and experiments become increasingly difficult due to fission competition. None-the-less, the first 2+ state in the light Rn isotopes is too high in excitation energy to represent a deformed structure. In fact, E4/E2 ratios are approximately 2.2, suggesting a vibrational structure. By studying the odd-neutron Rn isotopes, and odd-proton At (Z=85) and Fr (Z=87) isotopes, perhaps the neutron and proton degress of freedom may be understood. Studies of the light odd Rn isotopes have been performed with SASSYER.

Experimental data for the Ra isotopes suffers more. Yrast excitation energies, much less intruder structures, are not known for most of the light isotopes. Studies of the light Ra isotopes have been performed with SASSYER. Deformation effects are predicted to occur much closer to the N=126 closed shell than for Rn or Po;