  We prove the bounded packing property for any abelian subgroup of a group
acting properly and cocompactly on a CAT(0) cube complex. A main ingredient of
the proof is a cubical flat torus theorem. This ingredient is also used to show
that central HNN extensions of maximal free-abelian subgroups of compact
special groups are virtually special, and to produce various examples of groups
that are not cocompactly cubulated.
