Convertible Napping Desk

Too bad a video isn't available. This is like the perfect thing for a video example.

That its bottom heavy must be part of the trick since its vaguely conical

I want one!

The story behind the name is a tad creepy:

"It is mostly known in the folk culture as kis gömböc, a round creature in the loft that remained from a killed pig, which swallows everyone one after the other who goes to see what happened to the previous ones"

what about an egg?

Or what about Daruma Dolls, a centuries-old Chinese toy that rights itself no matter how you tilt it? In fact its the reference for a popular Chinese proverb about picking yourself up after a fall (metaphorically). Just doesn't seem very impressive, unless I'm missing something here.

Yeah, what about an egg? I was thinking the same thing. A thing shaped like an egg also rights itself up, no complicated math, no mail-order needed...

An egg doesn't right itself - it doesn't always end up resting on the same point no matter what orientation it starts in. You can see this yourself. Put an egg on the counter. Wait until it stops moving. Pick it up and mark the point it was resting on. Put it back down on another point. It won't end up resting on the same point, unless it has an air bubble that isn't along the axis of symmetry, in which case the object's density makes it self righting - which is what the challenge stated: "three-dimensional thingy that purely by dint of its /geometry/ had only one possible way to balance upright."

The point is that Weebles and Daruma Dolls rely on *varying density* to accomplish the feat. They have a center of gravity that is very low on account of a weighted or hollowed out section. This widget does it WITHOUT that -- it's got uniform density and the action is accomplished purely through external geometry.

I can't see how by any stretch of the imagination an egg rights itself -- the egg just rolls over on its side and can from that point roll around all over the place. If you plotted the locus of possible points the egg could rest on, you'd get a circle, not a single point.

A sphere would right itself, wouldn't it? You can't exactly determine which point is the top and which is the bottom. Well, you could, but it would be open to interpretation...