  The Voronoi tessellation is the partition of space for a given seeds pattern
and the result of the partition depends completely on the type of given pattern
"random", Poisson-Voronoi tessellations (PVT), or "non-random", Non
Poisson-Voronoi tessellations. In this note we shall consider properties of
Voronoi tessellations with centers generated by Sobol quasi random sequences
which produce a more ordered disposition of the centers with respect to the PVT
case. A probability density function for volumes of these Sobol Voronoi
tessellations (SVT) will be proposed and compared with results of numerical
simulations. An application will be presented concerning the local structure of
gas ($CO_2$) in the liquid-gas coexistence phase. Furthermore a probability
distribution will be computed for the length of chords resulting from the
intersections of random lines with a three-dimensional SVT. The agreement of
the analytical formula with the results from a computer simulation will be also
investigated. Finally a new type of Voronoi tessellation based on adjustable
positions of seeds has been introduced which generalizes both PVT and SVT
cases.
