A well-known and well-investigated family of hard optimization problems concerns variants of the cutting stock or nesting problem, i.e. the non-overlapping placing of polygons to be cut from a rectangle or the plane whilst minimizing the waste. Here we consider an in some sense inverse problem. Concretly, given a set of polygons in the plane, we seek the minimum number of rectangles of a given shape such that every polygon is covered by at least one rectangle. As motions of the given rectangle we investigate the cases of translation and of translation combined with rotation.