This is a first attempt at making an "Auxetic" material. When compressed in the vertical direction, it shows the rather unusual behavior of contracting in the other two directions. If one assigned a Poisson number to the assembly, it would be negative. You could consider this a "mechanical metamaterial". See Wikipedia for more information: http://en.wikipedia.org/wiki/Auxetics. Thanks to my friend Greg for introducing me to Auxetics.
Technical Note: Lots can be improved going from this first try: - compression in x/y leads to buckling: try introducing double parallel horizontal linkages to avoid - actually, a 3x3x3 unit (or whatever one can afford) would be cool, and might also help with the buckling - at maximum compression, the 4 hinges meet and interfere much less elegant than desired