[biot]

Presumably a simple sphere would trivially qualify as being unable to pass through itself.

[smokel]

The puzzle applies only to convex polyhedra.

[biot]

The article says:

> The full menagerie of shapes is too diverse to get a handle on, so mathematicians tend to focus on convex polyhedra

The phrase "tend to focus on" suggests it's not an exclusive thing. However, you're right -- it appears that the Rupert property only applies to convex polyhedra, so the article title and text is at the very least incomplete given that a sphere is a shape.

[LostMyLogin]

A sphere is not a convex polyhedron

[guelo]

At the limit of faces they are.