3-DIMENSIONAL SHAPE STATISTICS - APPLICATIONS

We apply the three-dimensional shape statistics developed in our previ ous paper to observations and simulations. We also develop an improved way of presenting the structures detected by the shape statistics ove r the one in the previous paper. We find significantly different clust ering properties between the CfA survey and the Pisces-Perseus Supercl uster survey on all scales we consider, implying that neither of them is a fair sample of the universe. Our results demonstrate that the sha pe statistics are powerful tools to detect clusters in a galaxy distri bution, to distinguish filaments from pancakes, to discriminate differ ent models of the large-scale structure, and to probe the dynamic evol ution of structure formation.