  A hinged dissection of a set of polygons S is a collection of polygonal
pieces hinged together at vertices that can be folded into any member of S. We
present a hinged dissection of all edge-to-edge gluings of n congruent copies
of a polygon P that join corresponding edges of P. This construction uses kn
pieces, where k is the number of vertices of P. When P is a regular polygon, we
show how to reduce the number of pieces to ceiling(k/2)*(n-1). In particular,
we consider polyominoes (made up of unit squares), polyiamonds (made up of
equilateral triangles), and polyhexes (made up of regular hexagons). We also
give a hinged dissection of all polyabolos (made up of right isosceles
triangles), which do not fall under the general result mentioned above.
Finally, we show that if P can be hinged into Q, then any edge-to-edge gluing
of n congruent copies of P can be hinged into any edge-to-edge gluing of n
congruent copies of Q.
