Geomagic Squares

The 16 pieces in the 4×4 square above are composed of 8 complementary pairs. Every pair tiles an identical shape that is one half of the target. The pairs can be seen in the bottom row of figures, any two of which will combine to complete the square target. In all there are 52 groups of four target-tiling pieces, only 48 of which are shown. The remaining four can be assembled using the four corner pieces belonging to each of the four embedded 3×3 sub-squares. Piece sizes run from 1 up to 17, but skip 9.