This is Awesome Stuff Other People Have Made Week on Overthinking My Teaching. So much great stuff to share.
Anyway, Curvahedra is a system of pinwheely spirally things that attach to each other in a simple and clever way, and which then allows you to build strange and interesting 3-dimensional objects. He brought samples along to Twitter Math Camp this past summer, and they are clearly quite wonderful.
If you are able, you should throw 10 bucks or more into the pot over at Kickstarter so you can play along when they ship next spring.