1 Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China; 
2 Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA; 
3 Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA; 
4 Department of Physics, Tsinghua University, Beijing 100084, China; 
5 Center of Nuclear Theory, Lanzhou National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, China; 
6 Department of Physics, Xiamen University, Xiamen 361005, China; 
7 Department of Physics, Chung Yuan Christian University, Chung-Li, Taiwan 32023, China

Angular-momentum-projected energy surface calculations for A ≈110 nuclei indicate three distinct energy minima occurring at different angular-momenta. These correspond to normal, super-, and hyper-deformed shapes coexisting in one nucleus. ¹¹⁰Pd is studied in detail, with a quantitative prediction on super- and hyper-deformed spectra by the Projected Shell Model calculation. It is found that several other neighboring nuclei in the A-110 mass region, with the neutron number around 64, also exhibit clear super- and hyper-deformation minima in the projected calculation.