It reminds me of a real life "problem" I like to solve around the holidays: what is the smallest cut of wrapping paper required to wrap a given box. With a restriction in one dimension.
I find that, most of the time for cube-ish boxes, using a somewhat diagonal orientation can result in a shorter cut of wrapping paper used, and reduces the amount of tape needed to keep it on the shape as well!
My mom did upholstery as a hobby; it only occurred to me in adulthood that wrapping paper isn’t designed so that the patterns would just magically line up somehow.
I like to use the offcuts of wrapping paper to make 'hidden' labels: trim the offcut to be 2x1 ratio rectangle; fold in half with pattern outside; pinch the crease sharp; write the name and message on the 'back' blank half; fold the tag in half again; position the 'front' pattern to exactly overlay a corresponding patch of pattern on the package; tape the back message half down to the package with transparent tape.
