  We investigate the supercluster shape properties of the all-sky observed
(Abell/ACO) and simulated (Virgo data) cluster catalogues using an approach
based on differential geometry. We reliably identify rich superclusters by
applying percolation statistics to both observed and mock cluster populations,
the latter being constructed following the observational requirements of the
Abell/ACO sample extended out to $z_{\rm max}\leq 0.114$. We apply a set of
shape diagnostics in order to study in a thorough way the morphological
features of superclusters with $\geq 8$ cluster members. Results demonstrate
that filamentarity is the dominant shape feature of superclusters. On comparing
data and models, we show that the $\Lambda$CDM ($\Omega_{\Lambda}=1-\Omega_{\rm
m}=0.7$) model performs better than $\tau$CDM, which is excluded at a high
confidence level, in agreement with other recent large scale structure studies.

Astrophysics