  The semiclassical origins of the enhancement of shell effects in exotic-shape
mean-field potentials are investigated by focusing attention on the roles of
the local symmetries associated with the periodic-orbit bifurcations. The
deformed shell structures for four types of pure octupole shapes in the nuclear
mean-field model having a realistic radial dependence are analyzed. Remarkable
shell effects are shown for a large Y32 deformation having tetrahedral
symmetry. Much stronger shell effects found in the shape parametrization
smoothly connecting the sphere and the tetrahedron are investigated from the
view point of the classical-quantum correspondence. The local dynamical
symmetries associated with the bridge orbit bifurcations are shown to have
significant roles in emergence of the exotic deformed shell structures for
certain combinations of the surface diffuseness and the tetrahedral deformation
parameters.
