The shape distribution of superclusters in SDSS DR 12
  Superclusters are the largest structures formed due to the gravitational
collapse and thus their geometrical information can shed light on the structure
formation process on cosmological scales, hence on the fundamental properties
of gravity itself. In this work we study the distributions of the shape,
topology and morphology of the superclusters, defined in two different ways --
using constant and individual density threshold on a luminosity weighted
density field constructed from SDSS DR 12 main galaxy sample. For this purpose,
we employ Minkowski functionals and Shapefinders, precisely calculated by the
shape diagnostic tool SURFGEN2. We notice a striking similarity in the shape
distributions of the supercluster samples those are obtained following these
two distinct techniques. Not surprisingly, most of them are spherical in shape
with trivial topology. But there are a significant number of superclusters that
are quite filamentary and statistically tend to be large in size with non-zero
genus values. The shape distribution results (catalogues) along with the
modified SURFGEN2 code have been made publicly available.
