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 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