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 _ { 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 _ { 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 .

Keywords : cosmology : theory - clusters - superclusters : general - large-scale structure of universe - Optical : clusters