We raise and investigate the following problem:
If the Euclidean
3-space is partitioned into convex cells each containing a unit ball,
how should the shapes of the cells be designed to minimize the
average surface area of the cells?
This problem leads to a strong
version of the Kepler conjecture on densest sphere packings as
well as to a new relative of Kelvin foam problem.
The talk is of a survey-type.