  Accounting for the triaxial shapes of galaxy clusters is expected to become
important in the context of the upcoming cosmological surveys. While the
distribution of matter in galaxy clusters cannot be described with simple
geometrical models without loss of information, their gravitational potential
can be very well approximated by a sphere or a spheroid. We study the shape of
the isodensity and isopotential contours in a relaxed and dynamically active
simulated clusters, with both a principal component analysis (PCA) and an
elliptical fitting procedure. We then analyze how the choice of the
substructure removal algorithm and the representation of the data (cumulative
vs thin shell) affect the results. For the matter distribution, we find that
the orientation and axis ratio of the isodensity contours are highly degenerate
with the presence of substructures and unstable against the representation of
the data. In addition, we observe that as the derived cluster shape depends on
the method used for removing the substructures, thermodynamic properties
extracted from, for instance, the X-ray emissivity profile, suffer from this
additional, and often underestimated, bias. In contrast, as the potential is
smoother and more spherical than the matter density, the PCA results on the
isopotential contours are robust against the choice of representations of the
data, and converge toward simple geometrical models for both the relaxed and
the dynamically active clusters. The fact that clusters potentials can be
represented by simple geometrical models and reconstructed with a low level of
systematics for both dynamically active and relaxed clusters (see Tchernin et
al. 2020), suggests that by characterizing galaxy clusters by their potential
rather than by their mass, dynamically active and relaxed clusters could be
combined in cosmological studies, improving statistics and lowering
scatter.[abr.]
