This definitely needs to be origamified:
George W. Hart:
A fold-up, slice-and-dice dodecahedron and its complement.
With a 3D printer, you can make your own using the files here
This is an awesome folding dodecahedron and its complement. Together they form a cube. Each is made of eight parts hinged together with white adhesive tape. To get a sense of it, see the video Inside-Out Logic on my YouTube channel. The stl files are here and here. You need to make four copies of each file and also four copies of the mirror image of each file. From the video, you can figure out how they get assembled.
Any geometric origami wiz up for the challenge?
Hat tip: Scott Cramer on the O-List