  In [4], Dunwoody defined resolutions for finitely presented group actions on
simplicial trees, that is, an action of the group on a tree with smaller edge
and vertex stabilizers. He, moreover, proved that the size of the resolution is
bounded by a constant depending only on the group. Extending Dunwoody's
definition of patterns we construct resolutions for group actions on a general
finite dimensional CAT(0) cube complex. In dimension two, we bound the number
of hyperplanes of this resolution. We apply this result for surfaces and
3-manifolds to bound collections of codimension-1 submanifolds.
