for nuclei with a large oblate g.s. deformation and a short triaxial barrier. The additional studies of the mass-asymmetry and higher nonaxial multipoles are described in the proper subsections of the Results section.

Thus, at the first stage, for all 1305 investigated nuclei the saddle points were searched in a five dimensional deformation space spanned by: $\beta_{20}$, $\beta_{22}$, $\beta_{40}$, $\beta_{60}$, $\beta_{80}$, using the IWF technique. The appropriate nuclear radius expansion has the form: $$\begin{aligned}
 \label{maingrid}
 R(\vartheta ,\varphi) &=& c(\{\beta\})R_0 \{ 1 + \beta_{20} {\rm Y}_{20}
 +\frac{\beta_{22}}{\sqrt{2}}\left[{{\rm Y}_{22} +
 {\rm Y}_{2 - 2}}\right]  \nonumber\\ &+&\beta_{40}  {\rm Y}_{40} +
  \beta_{60} {\rm Y}_{60} + \beta_{80} {\rm Y}_{80}  \}.\end{aligned}$$ The five-dimensional calculations are performed on the following deformation mesh: $$\begin{aligned}
\beta_{20} & = &  \ \  0.00 \ (0.05) \ 0.60    \nonumber \\
\beta_{22} & = &  \ \  0.00 \ (0.05) \ 0.45    \nonumber \\
\beta_{40} & = &  \ \  -0.20 \ (0.02) \ 0.20    \nonumber \\
\beta_{60} & = &  \ \  -0.10 \ (0.02) \ 0.10    \nonumber\\
\beta_{80} & = &  \ \  -0.10 \ (0.02) \ 0.10    \nonumber\\\end{aligned}$$ This makes a grid of 29250 points which was subsequently interpolated to a fivefold denser grid of 50735286 points with the 