  There exist four non-equivalent types of the translation hypersurfaces in the
4-dimensional isotropic space $\mathbb{I}^{4}$ generated by translating the
curves lying in perpendicular $k-$planes $\left(k=2,3\right)$, due to its
absolute figure. In arbitrary dimensional case; constant Gauss-Kronecker and
mean curvature translation hypersurfaces of type 1, i.e. the hypersurfaces
whose the translating curves lie in perpendicular isotropic $2- $planes, were
investigated by the same authors in \cite{AO}. The present study concerns such
hypersurfaces in $\mathbb{I}^{4}$ of other three types.
