We determine all Dehn-surgeries (see [1, 6, 7]) of Gieseking hyperbolic simplex manifold $\tilde S$, leading to compact orbifolds $\mathcal S(k)$ $k=2,3, \dots$ with singularity geodesics of rotation order $k$. We compute also the volume of $\mathcal S(k)$, tending to 0 if $k\to\infty$ (see our Table 2.1 and Figures 2.1-8).