Auxetic materials are a bit exotic in that, unlike all other substances, they get thicker when squeezed. Here is how an article"Auxetic Materials - An Introduction" by P.J. Stott, R. Mitchell, K. Alderson and A. Alderson abstracted in AZOM.com describes the effect:
Pick up an elastic band and stretch it lengthways as if you were going to `ping' it at somebody. Before letting fly, look at the width of your elongated missile - it's thinner than an unstretched band, as you'd expect. Try this with an auxetic elastic band and you'd be in for a surprise. These bizarre materials can actually become fatter when stretched, a phenomenon which is now attracting the practical interest of many materials scientists.
Here is a video that demonstrates the phenomena:
And here is a video demonstrating the same phenomenon using Auxetic foam:
It seems to me that there are some pretty cool toys that could be made using this material. If anyone is currently working with Auxetics let us know.
Thank you Andrew Gottlieb for bringing Auxetics to my attention