Clearly it's not an impossible shape.
Otherwise it would never have been made.
It is an unusual shape however.
Quote:Julie J. Rehmeyer :
Eventually, the team managed to construct an object mathematically that has just one stable and one unstable balance point.
That means that it can be balanced on one point and will be stable ie. it won't fall over if you let go of it.
That's the rounded or bottom part of it.
It has another balance point which is on the semi-circular ridge opposite the rounded part.
You can balance it on that too but as soon as you let go of it the thing will fall over and eventually will roll around until it's on the other more stable point.
If you had exceptional control you could balance it on the unstable side but the slightest movement of the air, vibration or any other interaction will make it fall over. Hence unstable balance point.
A bit like trying to balance an egg on the pointy end but much, much more difficult.
I am trying to obtain one for my collection of interesting objects.