Generating All Simple Convexly-Drawable Polar Symmetric 6-Venn Diagrams

摘要

An n-Venn diagram consists of n curves drawn in the plane in such a way that each of the 2~n possible intersections of the interiors and exteriors of the curves forms a connected non-empty region. A Venn diagram is convexly-drawable if it can be drawn with all curves convex and it is simple if at most two curves intersect at any point. A Venn diagram is called polar symmetric if its stereographic projection about the infinite outer face is isomorphic to the projection about the innermost face. We outline an algorithm that shows there are exactly 375 simple convexly drawable polar-symmetric 6-Venn diagrams.