  Geometry and mechanics have both a relevant role in determining the
three-dimensional packing of 8 bubbles displyaed in a foam structure. We assume
that the spatial arrangement of bubbles obeys a geometrical principle
maximizing the minimum mutual distance between the bubble centroids. The
compacted structure is then obtained by radially packing the bubbles under
constraint of volume conservation. We generate a polygonal tiling on the
central sphere and peripheral bubbles with both flat and curved interfaces. We
verify that the obtained polyhedra is optimal under suitable physical criteria.
Finally, we enforce the mechanical balance imposing the constraint of
conservation of volume. We find an anisotropy in the distribution of the field
of forces: surface tensions of bubble-bubble interfaces with normal oriented in
the circumferential direction of bubbles aggregate are larger than the ones
with normal unit vector pointing radially out of the aggregate. We suggest that
this mechanical cue is key for the symmetry break of this bubbles
configuration.
