There is a simple symmetric 5-Venn diagram in which each curve is a triangle; see this figure, redrawn from Grünbaum [Gr92b]. Grünbaum [Gr84b] asked whether there was a 6-Venn diagram made from triangles. This question was recently answered in the affirmative by Jeremy Carroll [Car00] - his first example is shown below. The diagrams on this page are all simple. He has subsequently discovered that there are exactly 126 different 6-Venn diagrams that can be drawn where each curve is a triangle.
Below is a table of coordinates for the six triangles.
Below is another nicer example (this jpeg image courtesy of Jeremy Carroll). See his web page [JC] for further examples like this.
