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Geometric method based on the high-order 3D Voronoi tessellation is proposed for identifying the single galaxies, pairs and triplets. This approach allows to select small galaxy groups and isolated galaxies in different environment and find the isolated systems. The volume-limited sample of galaxies from the SDSS DR5 spectroscopic survey was used. We conclude that in such small groups as pairs and triplets the segregation by luminosity is clearly observed: galaxies in the isolated pairs and triplets are on average two times more luminous than isolated galaxies. We consider the dark matter content in different systems. The median values of mass-to-luminosity ratio are 12 M_sol/L_sol for the isolated pairs and 44 M_sol/L_sol for the isolated triplets; 7 (8) M_sol/L_sol for the most compact pairs (triplets). We found also that systems in the denser environment have greater rms velocity and mass-to-luminosity ratio.
The construction of catalogues of galaxies and the a posteriori study of galaxy properties in relation to their environment have been hampered by scarce redshift information. The new 3-dimensional (3D) surveys permit small, faint, physically bound sa
We present a new open source code for massive parallel computation of Voronoi tessellations(VT hereafter) in large data sets. The code is focused for astrophysical purposes where VT densities and neighbors are widely used. There are several serial Vo
A homogeneous Poisson-Voronoi tessellation of intensity $gamma$ is observed in a convex body $W$. We associate to each cell of the tessellation two characteristic radii: the inradius, i.e. the radius of the largest ball centered at the nucleus and in
The Sloan Digital Sky Survey has obtained 450 square degrees of photometric scan data, in five bands (u,g,r,i,z), which we use to identify clusters of galaxies. We illustrate how we do star-galaxy separation, and present a simple and elegant method o
A jammed packing of frictionless spheres at zero temperature is perfectly specified by the network of contact forces from which mechanical properties can be derived. However, we can alternatively consider a packing as a geometric structure, character