%0 Journal Article
%T On packing spheres into containers (about Kepler's finite sphere packing problem)
%A Achill Schuermann
%J Mathematics
%D 2005
%I arXiv
%X In an Euclidean $d$-space, the container problem asks to pack $n$ equally sized spheres into a minimal dilate of a fixed container. If the container is a smooth convex body and $d\geq 2$ we show that solutions to the container problem can not have a ``simple structure'' for large $n$. By this we in particular find that there exist arbitrary small $r>0$, such that packings in a smooth, 3-dimensional convex body, with a maximum number of spheres of radius $r$, are necessarily not hexagonal close packings. This contradicts Kepler's famous statement that the cubic or hexagonal close packing ``will be the tightest possible, so that in no other arrangement more spheres could be packed into the same container''.
%U http://arxiv.org/abs/math/0506200v2