  We study static non-axial octupole deformations in proton-rich $Z=N$ nuclei,
$^{64}$Ge, $^{68}$Se, $^{72}$Kr, $^{76}$Sr, $^{80}$Zr and $^{84}$Mo, by using
the Skyrme Hartree-Fock plus BCS calculation with no restrictions on the
nuclear shape. The calculation predicts that the oblate ground state in
$^{68}$Se is extremely soft for the $Y_{33}$ triangular deformation, and that
in $^{80}$Zr the low-lying local minimum state coexisting with the prolate
ground state has the $Y_{32}$ tetrahedral deformation.
