It's Much Work, Measuring Turtles
This object, which is of uniform density, is self-righting. It has a second balance point that is "unstable"/highly susceptible to perturbation (when I first read the article I thought it said it didn't have such a point, which freaked me out). I love mathematical objects that are complex and yet arise from (presumably) simple causes (irrational numbers, Julia / Mandelbrot sets, etc.).
My favorite part of \<a href="http://blog.sciencenews.org/mathtrek/2007/04/cant_knock_it_down.html"" target="_blank" rel="noopener noreferrer">the article though, is that the mathematicians noted the similarity of the shape to certain turtle shells. They are now attempting to find if any turtles are inherently self-righting with no leg wiggling. But "It's much work, measuring turtles."
Original post by Fabian