The ComeBack Turtles

I'm not obsessed with the tortoise for nothing, you know. The shape of the Great Indian Tortoise might just be a mathematically unique structure. Normally, for a shape to be titlted and come back upright, the bottom needs to be heavier than the top. What if this balancing quality was not a property of the weight distribution, but of the very shape of the surface? If this article is correct, that is:

Now, Domokos and Várkonyi are measuring turtles to see if any of them are truly self-righting, or whether the turtles need to kick their legs a bit to flip themselves back upright. So far, they've tested 30 turtles and found quite a few that are nearly self-righting. Várkonyi admits that most biology experiments study many more animals than that but, he says, "it's much work, measuring turtles."

The mathematicians still face an unanswered question. The self-righting objects they've found have been smooth and curvy. They wonder if it's possible to create a self-righting polyhedral object, which would have flat sides. They think it is probably possible, but they haven't yet managed to find such an object. So, they are offering a prize to the first person to find one: $10,000, divided by the number of sides of the polyhedron.