calculations for many ($\sim$ 1000) nuclei. Including mass- and axially-symmetric deformations ($\beta_{20}$, $\beta_{40}$, $\beta_{60}$, $\beta_{80}$ - see [@Patyk1; @Patyk2; @Patyk3; @Smol1] together with both, mass-asymmetry ($\beta_{30}$, $\beta_{50}$, $\beta_{70}$) and triaxiality (at least $\beta_{22}$) would mean at least an eight-dimensional mesh and was impossible at present.

Based on our previous results showing that triaxial saddles are abundant in SH nuclei [@Kow], we consider that quadrupole triaxial shapes have to be necessarily included. We treated the effects of mass-asymmetry and nonaxial higher multipoles as corrections and analysed them at the second stage of calculations. A rationale for a lesser importance of mass-asymmetric saddles is that, while they constitute a second, more deformed ($\beta_{20}\approx
 0.7 - 0.8)$, prominent barrier peak in actinides, their heights are much reduced in SH nuclei where they become irrelevant. In the remaining, less deformed saddles the mass asymmetry occurs less frequently. As to the nonaxial multipoles of higher order, they are less important for saddles with small to moderate $\gamma$ \[where $\gamma$ is the Bohr’s quadrupole nonaxiality parameter, cf. Eq. (\[betgam\])\]. They become important for $\gamma$ closer to $60^o$ where they are needed to produce oblate shapes having $x$ as the symmetry axis. Thus, they should be included 