The olicognograph reproduces 4 times (on the plane) or a cube in a volume (could be 8sub-cubes) an expanded sort of Hedgeworth box, were the axis, more fondamentally than the share of goods 1 & 2 would better be the rights and duties in a broad social sense, (without defining them here). Complex plane can also be recalled in this frame like to make different sense or sign of rights and duties: their is at one time one real box of relations and other to consider if affected. Now, at the center the subject or you, but you may define it as you like. In our mind the essential unity of the social relations we all have or invent it of belief in.
Convexity of boerdering curves expresses then, the sort of relations you expect but you have to mind. Also that you depend on. As a result if you can expect to be globally convex, respect to outside in most essential relations, you may tolerate some partial concavity. In fact expressing like the sense of sacrifice, as for your children, according to the circumstances or for all your society.
Now the simple central ellipse here, does not suggest complexity, so it may missed it. There are the things about what for are the relations: many, so for variety, diversity and switches. If you cannot consider at one time everythings and have to focus on some, better not just one, since you can solve generally up to 4 degrees. There is no freedom of options if just one: for example when only your hunger for dollars.
Other patterns of borders are possible, like beehive's lines (hexagonal grid) in simply constrained environments (compact or dense places) or other pieces of lines as in Cournot-Nash or Stackelberg's equilibriums). Just an ability to dress such frames significant to your processes decisions can make you a smarter homoeconomicus (do not forget humane values).