  Within the self-consistent constraint Skyrme-Hartree-Fock+BCS model
(SHF+BCS), we found equilibrium toroidal nuclear density distributions in the
region of super-heavy elements. For nuclei with a sufficient oblate deformation
($Q_{20}\leq$ -200 b), it becomes energetically favourable to change the genus
of nuclear surface from 0 to 1, i.e., to switch the shape from a biconcave disc
to a torus. The energy of the toroidal (genus=1) SHF+BCS solution relative to
the compact (genus=0) ground state energy is strongly dependent both on the
atomic number Z and the mass number A. We discuss the region of Z and A where
the toroidal SHF+BCS total energy begins to be a global minimum.
