Inspired partly by a math project I did as a little kid and partly by Dulcet's icosahedron dice bag (https://www.craftster.org/forum/index.php?topic=322077.0
), I made an icosahedron and a dodecahedron out of straws to use as keychains. The icosahedron was made with paperclips and jump rings.
There's a paperclip in each end of each straw, linked into jump rings in sets of five.
I'm afraid my camera doesn't focus well up close. Anyway, they meet at the vertices in sets of five, and the clips are glued into the straws. That was really messy.
was made with rubber bands running through the straws:
To do this, I cut a rubber band, put a binder clip on one end, ran it through 5 straw pieces, took off the clip and tied it. Then I did that again, using one edge of my first pentagon as one of the edges of the second. Then I adjustified the rubber bands so the knots were inside the shared straw, where you can't see them but I won't poke any more bands through that one so the won't be in the way. Rubber bands are adjustified by work alone.
This method gives superior squashability in case someone steps on your keychain:
You can use this method for any solid; you need as many rubber bands as faces/as many jump rings as vertices and 5x as many paperclips as vertices. You need as many straw pieces as edges. (# of edges=number of faces x number of edges of shape of face divided by 2; # of vertices=number of faces x number of sides of shape of face divided by number of face that meet at each vertex)
This was really fun.
My family says I'm geeky.