We discuss the predictions of the large scale calculations using the realistic realisation of the phenomenological nuclear mean-field theory. Calculations indicate that certain Zirconium nuclei are tetrahedral-symmetric in their ground-states. After
a short overview of the research of the nuclear tetrahedral symmetry in the past we analyse the predictive capacities of the method and focus on the $^{96}$Zr nucleus expected to be tetrahedral in its ground-state.
