Shapes describing the alpha decay, cluster radioactivity, fusion, fission and fragmentation phenomena

To model the alpha decay, cluster radioactivity, fusion, fission and fragmentation phenomena of microscopic or macroscopic distributions of matter or charge it is useful to simulate these deformed physical objects by geometric shapes allowing the determination of their root mean square radius, volume, surface and Coulomb energies as well as their moments of inertia and quadrupole moments. Most of the shapes used in macroscopic nuclear physics are briefly recalled. In particular, several shape sequences that we have used previously, mainly formed from generalized lemniscatoids, are more extensively detailed. They allow us to describe the transitions from one compact configuration to several ones or vice versa. (paper)