Theoretical results on the ground-state properties of the hypothetical spherical superheavy atomic nuclei are presented and discussed. Even-even isotopes of elements Z=104-120 are considered. Certain conclusions are also drawn for odd-A and odd-odd superheavy nuclei. Results obtained earlier for even-even deformed superheavy nuclei with Z=104-114 are given for completeness. Equilibrium deformation, nuclear mass, α-decay energy, α-decay half-life, dynamical fission barrier, as well as spontaneous-fission half-life are considered. β-stability of superheavy nuclei is also discussed. The calculations are based on the macroscopic-microscopic model. A multidimensional deformation space describing axially symmetric nuclear shapes is used in the analysis of masses and decay properties of superheavy nuclei. We determined the boundaries of the region of superheavy nuclei which are expected to live long enough to be detected after the synthesis in a present-day experimental setup.