I'm a huge fidgeter. My hands want to be doing something all the time. Since I learned how to knit in middle school, my preferred method of fidgeting is working with yarn. It gives me an outlet for that energy that actually serves a purpose. I move my hands and then something appears!
Because of my penchant for all things yarn I learned about modeling complex maths back in high school. I didn't always pay attention to what was really going on in the articles I read, but the pictures looked cool. Still, it wasn't until my college hosted a version of this exhibit on hyperbolic space that I was motivated to make any of my own. The pictures don't do models justice. Seeing them behind glass it was so frustrating not to be able to pick them up. I did the only thing reasonable and started making my own.
The models are as amazing to play with as I'd hoped. Twisting. Turning. Following the edge around. My personal favorite creation (though it's mathematically insignificant) is a small hyperbolic plane, twisted and sewn together to become a moebius strip. I like it enough that I made one for a friend's birthday present.
Knowing that not every fidgeter finds an outlet for their energy, I decided to stock my classroom with fidget toys. The models are great because they're quiet. They're not impossible to throw--and my classroom management is still at a point where that's a consideration--but they're not going to hurt anyone if you do throw them. And they are math related!
I have not used them as much as I'd hoped before school started. Partly because I don't have the classroom set up so that they're accessible and visible. Partly because I only have one student who has fidgeting needs. He seems to like them, though I still need to figure out how to reach him with my lessons.