Nuclear Tetrahedral Symmetry: Possibly Present throughout the Periodic Table

More than half a century after the fundamental, spherical shell structure in nuclei had been established, theoretical predictions indicated that the shell gaps comparable or even stronger than those at spherical shapes may exist. Group-theoretical analysis supported by realistic mean-field calculations indicate that the corresponding nuclei are characterized by the $T_d^D$ (“double-tetrahedral”) symmetry group. Strong shell-gap structure is enhanced by the existence of the four-dimensional irreducible representations of $T_d^D$; it can be seen as a geometrical effect that does not depend on a particular realization of the mean field. Possibilities of discovering the $T_d^D$ symmetry in experiment are discussed.