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Shell-energy ridges and valleys caused by special symmetries for triaxial nuclear shapes.

The special degeneracy which occurs in the harmonic-oscillator potential when two of the frequencies have ratios of small integer numbers is exploited. Favored shell energies occur for particle numbers which vary with the third frequency. Applications to realistic nuclear potentials show that this degeneracy leads to special shell effects for axial shapes (1:1 ratio) but also for the 2:1 ratio exemplified by the triaxial ground state of /sup 24/Mg and triaxial superdeformed high-spin isomers in the light Hf nuclei.