To give it its full mathematical description, a Gömböc is a three-dimensional, convex and homogeneous object with exactly one stable point of equilibrium and one unstable point of equilibrium. Requiring it to be homogeneous amounts to saying that you’re not allowed to cheat: the material from which the Gömböc is made has to be uniform throughout, so you’re not allowed to use weights, as those found in roly-poly toys, or other irregularities to get the Gömböc to self-right. Convexity means that the Gömböc is not allowed to bulge inwards, in other words, the straight line connecting any two points on the Gömböc has to lie entirely within the Gömböc. It’s easy to create a non-convex shape with one stable and one unstable equilibrium point, hence the restriction to convexity.
I have this mental image of Dieter describing the Gömböc. I don’t know why.
Your three-dimensional, convex homogeneity has grown tiresome. Now is the time on Sprockets vhen ve dance!