The unstable N=42 nucleus ⁷²Zn has been studied using multiple safe Coulomb excitation in inverse kinematics. The experiment was performed at the REX-ISOLDE facility at CERN making first use of the silicon detector array C-REX in combination with the γ-ray spectrometer Miniball. The high angular coverage of C-REX allowed to determine the reduced transition strengths for the decay of the yrast 0₁⁺, 2₁⁺ and 4₁⁺ as well as of the 0₂⁺ and 2₂⁺ states in ⁷²Zn. The quadrupole moments of the 2₁⁺, 4₁⁺ and 2₂⁺ states were extracted. Using model independent quadrupole invariants, the ground state of ⁷²Zn was found to have an average deformation in the γ degree of freedom close to maximum triaxiality. In comparison to experimental data in zinc isotopes with N<40, the collectivity of the 4₁⁺ state in neutron-rich ⁷²Zn is significantly larger, indicating a collective yrast band based on the ground state of ⁷²Zn. In contrast, a low experimental B(E2;0₂⁺ → 2₁⁺) strength was determined, indicating a different structure for the 0₂⁺ state. Shell-model calculations propose a 0₂⁺ state featuring a larger fraction of the (spherical) N=40 closed-shell configuration in its wave function than for the 0₁⁺ ground state.
The results were also compared with beyond mean field calculations which corroborate the large deformation in the γ degree of freedom, while pointing to a more deformed 0₂⁺ state. These experimental and theoretical findings establish the importance of the γ degree of freedom in the ground state of ⁷²Zn, located between the ^68,70Ni nuclei that have spherical ground states, and ⁷⁶Ge, which has a rigid triaxial shape.