Many people are surprised to learn that Venn diagrams can be drawn to represent all of the intersections of more than three sets. This surprise is perfectly understandable since small Venn diagrams are often drawn with circles, and it is impossible to draw a Venn diagram with circles that will represent all the possible intersections of four (or more) sets. This is a simple consequence of the fact that circles can finitely intersect in at most two points and Euler’s relationF−E+V = 2 for the number of faces, edges, and vertices in a plane graph. However, there is no reason to restrict the curves of a Venn diagram to be circles; in modern definitions a Venn diagram is a collection of simple closed Jordan curves.This collection must have the property that the curves intersect in only finitely many points and the property that the intersection of the interiors of any of the 2n sub-collections of the curves is a nonempty connected region. If a Venn diagram consists ofncurves then we callitann-Venn diagram.Therank ofaregionisthe number of curves that contain) it. In anyn-Venn diagramthereareexactly regionsofrankr.Figure1 n r shows a 2-Venn and two distinct 3-Venn diagrams. Note thatthe diagraminFigure 1(c) hasthree points where all three curves intersect. The regions in the diagramsof Figure 2 are colored according to rank. The traditional three-circle Venn diagramhas an appealing 3-fold rotational symmetry, and it is natural to ask whether there aren-Venn diagramswith ann-foldrotationalsymmetryforn>3.Grünbaum [6] found a symmetric 5-Venn diagram made from ellipses. Henderson [10] noted the following necessary condition: if ann-Venn diagram has ann-fold rotational symmetry, thennis prime. The reason is asfollows: