  For the binary discs packed in two dimensions, the packing fraction of disc
assembly becomes lower than that of the monodisperse system when the size ratio
is close to unity. We show that the suppressed packing fraction is caused by an
increase of the adjacent neighbours with long bonds where the adjacent
neighbours is defined on the basis of the Laguerre (radical) tessellation. For
the poly-disperse systems in two and three dimensions, the packing fraction is
shown to have a minimuma as a function of the poly-dispersity. Percolation
process in the densely packed discs and spheres is also studied. The critical
area (volume) fraction in two (three) dimensions is shown to be a monotonically
increasing (decreasing) function of the poly-dispersity.
