Shape statistics of Sloan Digital Sky Survey superclusters

We study the supercluster shape properties of the recently compiled SDSS cluster catalog using an approach based on differential geometry. We detect superclusters by applying the percolation algorithm to observed cluster populations, extended out to $z_{\rm max}\leq 0.23$ in order to avoid selection biases. We utilize a set of shapefinders in order to study the morphological features of superclusters with $\geq 8$ cluster members and find that filamentary morphology is the dominant supercluster shape feature, in agreement with previous studies.