Here is a puzzle based on the dissection of a hexagon into five pieces which can be rearranged to form a square. Given the five pieces the problem is to assemble them into first a square and then a hexagon. Two trays, one square and one hexagonal, are included as aids and storage for the pieces.
This dissection of a hexagon into a square used a method described by Harry Lindgren. Images of squares and hexagons are formed into parallelogram "strips" and superimposed. One strip is rotated and shifted against the other until a solution is found. The diagram above illustrates this. More detail is in the openSCAD code.