FIGURE CAPTIONS
Figure 1: About 150000 equally sized spheres packed in a cylindrical container.
Figure 2:
(a) Normalized radial distribution function. (b) The detail of the two
peaks respectively at r /d  2 and r/d= 2 (vertical lines). (c) Ratio between the
value of the peak at r/d=2 and the peak at r /d  3 v.s. packing density.

 (spheres between two planes in this case)
Figure 3: In two dimensions, disks
tend to form spontaneously local hexagonal patterns which can be combined
globally leading to a crystalline order. On the other hand, in three dimensions the
resulting structures do not show any crystalline order, even at local level.
Figure 4: (a) The dots are the values of (Q4,Q6) plotted for all the local
configurations in the central region (G) of sample ‘C’. The lines are contour plots
of the frequencies, reported in the 3D plot of figure (b). The positions of specific
symmetries in the (Q4,Q6) plane are indicated (ico, bcc, fcc).
Figure 5: Dihedral angle distribution (x-axis: angular degrees; y-axis:
renormalized frequencies). The vertical lines indicate the angles  =n arccos(1/3)
(and 360-) with n=1,2,3,4,5 (tetrahedral packings). The dashed lines are at the
angles   n
360
(n=1,2,3,4), which will correspond to icosahedral
5
configurations.

Figure 6: (a) Distribution of Delaunay volumes in G. (b) The inverse normalized
cumulants show tails that decrease linearly in semi-logarithmic scale: p(v
exp(-
v/d3) (best-fits: =43.9; 45.4; 55.2; 64.6; 66.8; 72.9).
Figure 7:
Distribution of the number of near neighbors at radial distances within
1.05 diameters. The tick line is the theoretical behavior predicted by a freevolume like local theory: p(n) (4  4 n /n* )n with n*=12.99 (see Eq.4 in Aste
2005).

Figure 8:
(symbols) Average number of sphere centers within a radial distance
r. (lines) Complementary error function, normalized to nc by best-fitting the
agreement with the data in the region r/d <1. The averages (r=d) and the
standard deviations are calculated from the probability distribution for radial
distances smaller than d between pair of centers. The re-normalized
complementary error function fits well the data for r/d<1. After this value nearneighbors not in contact start to contribute significantly to nt(r) and the two
behaviors split. The ‘deconvoluted’ plots show the differences between nt(r) and
the fits with the complementary error functions normalized to nc. Data from (Aste,
Saadatfar & Senden, 2005).
Figure 9:
Number of neighbors in contact v.s. sample density. The filled
symbols correspond to the samples investigated in the present work. The two
symbols ‘+’ are the values from Bernal (1960) whereas the ‘X’ is from Scott
(1962) and Mason (1968).
Figure 10: Same as Fig.1 (with a piece removed) where the topological
distances from a given central sphere is highlighted in different gray tones.
Figure 11: Shell occupation numbers vs. topological distance. The symbols
indicate the different samples (as in Fig.8) and the lines are the best-fits using
the polynomial form: Kj=aj2+c1j+c0. The fits are between j=2 and j= ˆj = 10 (for
samples B, D, E, F ) and ˆj = 15 (for samples A, C). The data refer to threshold

distance 1.05d.

Figure 12: The coefficient a, plotted as a function of the average coordination
number of the contact network (n), shows that disordered packings have larger
topological densities in comparison with lattice sphere packings.
Figure 13: Total number of sphere centers in a cluster made by all the spheres
with centers within a given radial distance r from a given sphere. The thick lines
are the average cluster sizes in (G) for samples A-F. The thin lines are the
clusters with maximum/minimum number of spheres at a given distance. The
filled area is bounded at the top by the most efficient (largest numbers of
spheres) packings among the Mackay Icosahedron (Mkly) and the lattices fcc,
hcp, bcc, sc.
Figure 14: Log-log plot of the average number of sphere centers within a radial
distance r from a given sphere for the 6 samples (symbols). The full lines are
number of sphere centers within a radial distance r from a given sphere for the
Mackay Icosahedron (Mkly) and the lattices fcc, hcp, bcc, sc.
Figure 15: Average Isoperimetric Quotients (36(Volume)2/(Surface Area)3) v.s.
number of particles in the clusters formed by all the spheres within a radial
distance from a given central sphere. The empty square symbols correspond to
ordered and crystalline packings (Mkly, fcc, bcc, hcp, bcc, sc).