I meant to post this contribution to Thingadailies last night, but I just couldn't get it to behave. So rather than crumpling it up and tossing it in the trash, I went to bed. I picked it up this morning and looked at it closely and AHA! I folded one of the units wrong. Luckily I didn't have to put the whole thing apart; I just pulled out the miscreant unit, folded it into submission, and it slipped right into place. Isn't it amazing how easily things work when you do them right?
Anyway, a still picture doesn't do it justice, so here's a little video of my 12-unit icosehedron. (Those are the coffee table legs in the background.)