  Although most nuclear spectroscopy as well as atomic hyperfine structure data
do not deliver accurate information on nuclear axiality the ad-hoc assumption
of symmetry about one axis found widespread use in nuclear model calculations.
In the theoretical interpretation of nuclear properties as well as in the
analysis of experimental data triaxiality was considered - if at all - only for
some, often exotic, nuclides. A breaking of axial symmetry combined to a
spin-independent moment of inertia results in a surprisingly simple heuristic
triaxial parametrization of the yrast sequence in all heavy nuclei, including
well deformed ones. No additional fit parameters are needed in detailed studies
of the mass and charge dependence of the electric dipole strength in the range
of and outside of giant dipole resonances. Allowing triaxiality also avoids the
introduction of an arbitrary level density parameter \=a to fit the accurate
values observed in n-capture experiments and \=a can be taken from nuclear
matter studies. A combination of this value to the yrast energies no longer
based on axiality and the related I(I+1) rule results in agreement to data
independent of spin. And predictions for radiative neutron capture as derived
on the basis of non-axiality are improved as well. The experimentally favoured
broken axial symmetry is in accord to HFB and MC-shell model calculations
already for nuclei in the valley of stability.
