Packing density

Summary

The packing density of a packing is the fraction of space covered by its bodies. It is measured inside large balls and passed to the limit, since space is infinite. The packing density of a body is the largest density of a packing of its congruent copies. For equal balls this is the optimal sphere packing density, known exactly only in dimensions $1$, $2$, $3$, $8$ and $24$.