We say that two planar convex bodies *cross* if their union minus their intersection has more than two connected components.
(Here we suppose that their boundaries are nice and intersect in finitely many points.)
If no two member of a collection of bodies cross, then this is also called a *pseudodisk arrangement*.
I would like to know if given seven points in the plane whether it is possible to find $\binom 73$ pairwise non-crossing convex bodies, such that for each triple of the seven points there is a convex body containing exactly them from the set of seven points.
I'm also interested in what kind of theorems there are to conclude the non-existence of such embeddings.