Not sure if this is what you're thinking, and it would need some finishing touches, but:
Maybe make a TeePee shaped thing, with shelves in various places to hold in the wedges.
For the wedges themselves you could get some old couch cushions (good will?) and cut them into the proper shape and then get some fabric to cover them with.
Check out your local craft store to see if they have styrofoam shapes that you could use and just cover them.
You'd still need to design the triange to fit them in.
Jennifer and the monsters