Definition of Hinged Dissections

       In order to distinguish all kinds of hinged dissections in the content, different types of hinged dissections are illustrated in the beginning and more details of swing-hinged dissections are presented later.

　　

Types of hinged dissections:

n Swing hinge:

       For swing-hinged dissection of two pieces, we mean that the pieces stay in the plane as we swing them around on their hinges. Thus we turn over no pieces when we use swing hinges (Frederickson, 1997). Example such as the figure on the right, the dots indicate the hinges.

　

  

n Flip hinge:

        A flip hinge is a piece rotating 180° through the third dimension along a vertex that connects the two pieces (Frederickson, 1997). This figure shows the flip hinge where the star “*” indicates the turning pieces and the small circle “。” indicates the rotation vertex.

   

n Twist hinge:

        A twist hinge is of a piece rotating 180° through the third dimension along an axis of rotation that is perpendicular and interior to a shared edge (Frederickson, 1997). As shown in this figure, while the star “*” indicates the turning pieces and the small circle “。” on the edges indicates where the rotation axis is perpendicular to.

　

　

Hinge patterns in swing-hinged dissections:

        In swing-hinged dissections, we do more details on how many pieces hinging in the dissections or what kinds of swing-hinged patterns we referred to.

　

n  Partially hinged:

        For some dissections we can hinge most, rather than all, of the pieces. We shall call such a dissection partially hinged (Frederickson, 1997). Examples such as a pentagon to a triangle; an octagon to a square.

　

n  Fully hinged:

       A dissection is fully hinged if all pieces were connected with hinges into a chain so that rotating the pieces around one way assembles them into one of the figures of the dissection, and rotating the pieces the other way assembles them into the other figures of the dissection (Frederickson, 1997). Examples such as a square to a triangle, a dodecagon to a square.

　

n  Variously hinged:

        A dissection is variously hinged if we can hinge it with the largest possible number of hinges in several different ways (Frederickson, 1997). Examples such as a square to a triangle ; a Greek Cross to a square.

　

n Cyclicly hinged:

        If we can remove a set of hinged pieces without disconnecting them, we shell call this dissection cyclicly hinged (Frederickson, 1997). Examples such as a Greek Cross to a hexagon; two hexagons to a hexagon.

  

　

　
 
 　

Main