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 different body containing them all. I'm also interested in what kind of theorems there are to conclude the non-existence of such embeddings.