This object prints in one piece without raft or support, fully assembled, hinges and all! The resulting model will hinge from a square to a triangle and back again.
The model is based on Dudeney's famous hinged dissection known as the "Haberdasher's Puzzle". For more information, see MakerHome, Day 188.
Be sure to print with no raft and no support or the model will not work correctly. After printing you need to give the hinges a little "snap" to get them started.
This model is optimized for printing on a Replicator 2 with .3mm/low resolution. If you have problems printing on a different machine then tell me details in the comments and I will post some tighter/looser variants that might work better.
UPDATE: New post about this model, new versions for 3D printing on different printers, and new mathematical advances, at Hacktastic: Hinged Triangle-Square
Don't have a 3D printer, or want something fancy? Get this model from Shapeways:
Hacktastic blog: www.mathgrrl.com/hacktastic
Shapeways geekhaus store: www.shapeways.com/shops/mathgrrl
This design has a Creative Commons Attribution Share Alike license, which means that you can print, remix, and use this model with design credit to mathgrrl, but if you want to sell something then you should ask first, at firstname.lastname@example.org.