Here’s something silly and not-quite-entirely-useless for a Monday morning.
Think of a deformable material (something solid but something you can squeeze, stretch, dent, etc). Maybe a bean bag, lump of plasticine, football etc. It might or might not return to its original position after you let go of it, but that doesn’t matter. Think what happens if you squeeze it. It gets shorter in one direction, the direction you squeeze it in, but it splurges outwards in the other direction. This isn’t surprising, since many things pretty well conserve their volume when you derform them – if you push them in one direction they grow in the others.
Now find a cork (what used to go in the top of wine bottles before screwcaps). Squeeze it on the ends. It gets thinner.That’s pretty unusual in materials. Cork has a negative Poisson ratio – the Poisson ratio describes the negative of the ratio of transverse strain (the deformation along the non-squash dimensions) to transverse strain (the deformation along the dimension of squash). That means that a cork is easy to put into a wine bottle – squash it and it gets thinner – but not so easy to pull out, because when you pull it it gets thicker and grips the neck of the bottle.
Such materials can also be made with origami. A work colleague once demonstrated one to me. Pretty bizarre to play with. But it has its uses, like the collapsible stents described in the link here . If you’re good with your fingers, have a go at building one.