While working on my foil, I rediscovered a few interesting shapes I thought I'd share with you guys:
Gömböc - the only known convex and homogeneous shape with just one stable and one unstable point of balance.
Yoshimoto Cube - actually two stellated rhombic dodecahedrons (mouthful, I know) that fit perfectly within each other to form a cube.
Sphericon - a three-dimensional shape with one side and two edges. Can fit together to make interesting systems that rotate around each other called lattices. It uses a trick similar to moebius strips (rotate and reattach) and klein bottles (invert and reattach) to get its one surface from a bicone.
Also, here's the animation of a universal joint I modeled my aluminum foil piece from. I think it's quite pretty.
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