Introduced by the logician John Venn in 1880, Venn diagrams with n ≤ 3 curves have been the staple of many finite mathematics and other courses. Over the last decade the interest in Venn diagrams for larger val ues of n has intensified (see, for example, Ruskey [8] and the many refe rences given there). In particular, considerable attention has been devote d to symmetric Venn diagrams. A Venn diagram with n curves is said to be symmetric if rotations through 360/n degrees map the family of c urves onto itself, so that the diagram is not changed by the rotation. Thi s concept was introduced by Henderson [7], who provided two examples of non-simple symmetric Venn diagrams; one consists of pentagons, the o ther of quadrangles, but both can be modified to consist of triangles. A s imple symmetric Venn diagram consisting of five ellipses was given in [5]. As noted by Henderson, symmetric Venn diagrams with n curves canno t exist for values of n that are composite. Hence n = 7 is the next valu e for which a symmetric Venn diagram might exist. Henderson stated in [ 7] that such a diagram has been found; however, at later inquiry he could not locate it, and it was conjectured in [5] that such diagrams do not exis t.
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