1. Instituut voor Kern- en Stralingsfysica, University of Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium
2. Gesellschaft fur Schwerionenforschung Darmstadt, Postfach 110541, D-6100 Darmstadt, Germany
3. Department of Nuclear Physics, Comenius University, Bratislava, Slovakia
4. Department of Physics, Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE , UK
5. Department of Physics, University of Jyväskylä, FIN-40351 Jyväskylä , Finland
6. Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, 141980 Dubna, Russia
7. Department of Physics, Royal Institute of Technology, 104 05 Stockholm, Sweden, and
8. Department of Technology, Kalmar University, Box 905 , 391 29 Kalmar, Sweden
9. Vakgroep Subatomaire en Stralingsfysica, Institute for Theoretical Physics, B-9000 Gent, Belgium

Correspondence to: M. Huyse¹ Correspondence and requests for materials should be addressed to M.H. (e-mail: Email: mark.huyse@fys.kuleuven.ac.be).

Understanding the fundamental excitations of many-fermion systems is of significant current interest. In atomic nuclei with even numbers of neutrons and protons, the low-lying excitation spectrum is generally formed by nucleon pair breaking and nuclear vibrations or rotations. However, for certain numbers of protons and neutrons, a subtle rearrangement of only a few nucleons among the orbitals at the Fermi surface can result in a different elementary mode: a macroscopic shape change^{1, 2, 3}. The first experimental evidence for this phenomenon came from the observation of shape coexistence in ¹⁶O (ref. 4). Other unexpected examples came with the discovery of fission isomers⁵ and superdeformed nuclei⁶. Here we find experimentally that the lowest three states in the energy spectrum of the neutron deficient nucleus ¹⁸⁶Pb are spherical, oblate and prolate. The states are populated by the -decay of a parent nucleus; to identify them, we combine knowledge of the particular features of this decay⁷ with sensitive measurement techniques (a highly efficient velocity filter⁸ with strong background reduction, and an extremely selective recoil--electron coincidence tagging method^{8, 9, 10}). The existence of this apparently unique shape triplet is permitted only by the specific conditions that are met around this particular nucleus.