Most atomic nuclei are deformed with a quadrupole shape described by its overall strength β2 and triaxiality γ. The deformation can be accessed in high-energy heavy-ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity ε2 and the density gradient d⊥ in the initial state. Using analytical estimate and a Glauber model, we show that the variances, ⟨ε 2 2 ⟩ or ⟨(δd⊥ d⊥) 2 ⟩, and skewnesses, ⟨ε 2 2 δd⊥ d⊥⟩ or ⟨(δd⊥ d⊥From these, we constructed several normalized skewnesses to isolate the γ dependence from that of β2, and show that the correlations between a normalized skewness and a variance can constrain simultaneously the β2 and γ. Assuming a linear relation with elliptic flow v2 and mean-transverse momentum [p T ] of final state particles, v2 ∝ ε2 and δd⊥ d⊥ ∝ δ[p T ] [p T ], similar conclusions are also expected for the variances and skewnesses of v2 and [p T ], which can be measured precisely in top RHIC and LHC energies. Our findings motivate a dedicated system scan of high-energy heavy ion collisions to measure triaxiality of atomic nuclei. This is better done by collisions of prolate, cos(3γ) = 1, and oblate nuclei, cos(3γ) = −1, with well known β2 values to calibrate the coefficients b ′ and c ′ , followed by collisions of species of interest especially those with known β2 but unknown γ.