 There are certain implications among these, both obvious (for example, if a polyomino tiles the half plane then it tiles the whole plane) and less so (for example, if a polyomino tiles an enlarged copy of itself, then it tiles the quadrant).Polyominoes of orders up to 6 are characterized in this hierarchy (with the status of one hexomino, later found to tile a rectangle, unresolved at that time).In 2001 Cristopher Moore and John Michael Robson showed that the problem of tiling one polyomino with copies of another is NP-complete.