The question Floating polyhedra with fair equilibria was answered by Bill Thurston, but his (typically amazing) answer contains links to 7 figures, all now broken. I don't know how to retrieve those images from the past, but if someone does know how and is willing to spend the time & effort, it would be a nice contribution to the MathOverflow community.
Here are the other MO posts by Bill Thurston with missing pictures:
https://mathoverflow.net/a/38025
https://mathoverflow.net/a/39304
https://mathoverflow.net/a/39551
https://mathoverflow.net/a/39571
https://mathoverflow.net/a/39607
https://mathoverflow.net/a/50607
https://mathoverflow.net/a/50816
https://mathoverflow.net/a/51017
https://mathoverflow.net/a/51042
https://mathoverflow.net/a/52875
https://mathoverflow.net/a/52973