  Recent measurements have established the sensitivity of ultracentral
heavy-ion collisions to the deformation parameters of non-spherical nuclei. In
the case of ${}^{ 129}$Xe collisions, a quadrupole deformation of the nuclear
profile led to an enhancement of elliptic flow in the most central collisions.
In ${}^{ 208}$Pb collisions a discrepancy exists in similar centralities, where
either elliptic flow is over-predicted or triangular flow is under-predicted by
hydrodynamic models; this is known as the $v_2$-to-$v_3$ puzzle in ultracentral
collisions. Motivated by low-energy nuclear structure calculations, we consider
the possibility that $^{208}$Pb nuclei could have a pear shape deformation
(octupole), which has the effect of increasing triangular flow in central PbPb
collisions. Using the recent data from ALICE and ATLAS, we revisit the
$v_2$-to-$v_3$ puzzle in ultracentral collisions, including new constraints
from recent measurements of the triangular cumulant ratio
$v_3\left\{4\right\}/v_3\left\{2\right\}$ and comparing two different
hydrodynamic models. We find that, while an octupole deformation would slightly
improve the ratio between $v_2$ and $v_3$, it is at the expense of a
significantly worse triangular flow cumulant ratio. In fact, the latter
observable prefers no octupole deformation, with $\beta_3\lesssim 0.0375$ for
${}^{ 208}$Pb, and is therefore consistent with the expectation for a
doubly-magic nucleus even at top collider energies. The $v_2$-to-$v_3$ puzzle
remains a challenge for hydrodynamic models.
