In Vicious Circles there's a section on "nets" which are flat shapes that fold into solid lumps. Our friend Liz Meenan who is Channel 4's origami queen showed us how to make this extremely pleasing little toy... 4k185v
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You need two bits of card - one slightly bigger one to be the "backing" (shown here in blue) and one bit to make the cube net.
Cut out the cube net as shown by the YELLOW shape. Fold it and open it along all the dotted lines a few times so that it gets quite floppy.
Make four little holes and thread a long loop of string through them as indicated by the red line.
Position your net on the backing and then glue the bottom square to the backing as shown.
PULL THE STRING!
Be honest - isn't that great?
You can use a similar method to make an octohedron net assemble itself in the same way!