The signatures of rigid triaxiality in low-energy, low-spin nuclear spectra are discussed. Eight nuclei in the range of structural parameter 2.9 < R-4/2 < 3.3 are explored to find out whether they are gamma-static. Interestingly, this region is a transition path between X(5) critical point and the rigid rotor limit which is described by the confined beta-soft (CBS) rotor model of Pietralla and Gorbachenko (2004 Phys. Rev. 70 011304).
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