  Most atomic nuclei are deformed with a quadrupole shape described by its
overall strength $\beta_2$ and triaxiality $\gamma$. 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 $\varepsilon_2$
and the density gradient $d_{\perp}$ in the initial state. Using analytical
estimate and a Glauber model, I show that the variances,
$\langle\varepsilon_2^2\rangle$ or $\langle(\delta
d_{\perp}/d_{\perp})^2\rangle$, and skewnesses, $\langle\varepsilon_2^2\delta
d_{\perp}/d_{\perp}\rangle$ or $\langle(\delta d_{\perp}/d_{\perp})^3\rangle$,
have a simple analytical form of $a'+b'\beta_2^2$ and
$a'+(b'+c'\cos(3\gamma))\beta_2^3$, respectively. From these, I constructed
several normalized skewnesses to isolate the $\gamma$ dependence from that of
$\beta_2$, and show that the correlations between any normalized skewness and
any variance can constrain simultaneously the $\beta_2$ and $\gamma$. Assuming
a linear relation with elliptic flow $v_2$ and mean-transverse momentum
$[p_{\mathrm{T}}]$ of final state particles, similar conclusions are also
expected for the variances and skewnesses of $v_2$ and $[p_{\mathrm{T}}]$. 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, $\cos(3\gamma)=1$, and oblate nuclei, $\cos(3\gamma)=-1$, with well
known $\beta_2$ values to calibrate the coefficients $b'$ and $c'$, followed by
collisions of species of interest especially those with known $\beta_2$ but
unknown $\gamma$. The results demonstrate the unique opportunities offered by
high-energy collisions as a tool to perform interdisciplinary nuclear physics
studies.
