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. 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 isomers and super-deformed nuclei. 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 alpha-decay of a parent nucleus; to identify them, we combine knowledge of the particular features of this decay with sensitive measurement techniques (a highly efficient velocity filters with strong background reduction, and an extremely selective recoil-alpha-electron coincidence tagging methods). The existence of this apparently unique shape triplet is permitted only by the specific conditions that are met around this particular nucleus.