[hinkley]

It’s both. To work you need a polyhedron constructed of a series of polygons, here triangles, and one of those triangles has to have its center of mass outside the base of the object in all orientations. Otherwise the weight will pin it down instead of tilt it over.

That’s why in the one orientation it tips back before tipping sideways: the center of mass is inside the footprint of right edge of the tetrahedron but not the back edge. So it tips back, which then narrows the base enough for it to tip over to the right and settle.

[jrowen]

The article does a good job of explaining that it's still a non-trivial problem even if you are allowed to distribute the weight unevenly, but I do agree that what is happening here is much more specific than a "shape," which is simply geometry without any density information.

Put another way, most things precisely constructed with that same exact shape (of the outer hull, which is usually what is meant by shape) would not exhibit this property.

[kamel3d]

A ball that has a weight attached to one point from the inside would always land on that side, it's the same thing, right?

[degamad]

Correct - we knew we could do that with balls, but can you do it with a pyramid? It initially seems like there would always be at least two stable surfaces for a pyramid, but this group managed to figure out how to do it with only one stable surface.

[Vvector]

Last time I checked, spheres are shapes.

But the article references a "pyramid-like shape"

[Nition]

Yeah, but the challenge in this case was to achieve it without any rounded edges.