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We search for effects of tetrahedral deformation $\beta_{32}$ over a range of$\sim 3000$ heavy and superheavy nuclei, $82\leq Z \leq 126$, using amicroscopic-macroscopic model based on the deformed Woods-Saxon potential, welltested in the region. We look for the energy minima with a non-zero tetrahedraldistortion, both absolute and conditional - with the quadrupole distortionconstrained to zero. In order to assure reliability of our results we include10 most important deformation parameters in the energy minimization. We couldnot find any cases of stable tetrahedral shapes. The only sizable - up to 0.7MeV - lowering of the ground state occurs in superheavy nuclei $Z\geq 120$ for$N=173-188$, as a result of a {\it combined} action of two octupoledeformations: $\beta_{32}$ and $\beta_{30}$, in the ratio$\beta_{32}/\beta_{30}\approx \sqrt{3/5}$. The resulting shapes are moderatelyoblate, with the superimposed distortion $\beta_{33}$ {\it with respect to theoblate axis}, which makes the equator of the oblate spheroid slightlytriangular. Almost all found conditional minima are excited and not protectedby any barrier, a handful of them are degenerate with the axial minima.

Effect of tetrahedral shapes in heavy and superheavy nuclei