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This page gives a few examples of Venn diagrams for 4 sets. Some examples:
alt text alt text
Thinking about it for a little, it is impossible to partition the plane into the $16$ segments required for a complete $4$-set Venn diagram using only circles as we could do for $<4$ sets. Yet it is doable with ellipses or rectangles, so we don't require non-convex shapes as Edwards uses.

So what properties of a shape determine its suitability for $n$-set Venn diagrams? Specifically, why are circles not good enough for the case $n=4$?

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    Related: [6 sets is possible with triangles](http://www.combinatorics.org/Surveys/ds5/VennTriangleEJC.html), but [not 7](http://www.combinatorics.org/Surveys/ds5/VennGeometricEJC.html). Also, [a paper](http://www.google.com/url?sa=t&source=web&cd=2&ved=0CBgQFjAB&url=http%3A%2F%2Fwww.brynmawr.edu%2Fmath%2Fpeople%2Fanmyers%2FPAPERS%2FVenn.pdf&ei=UpRYTMf-HIminQfm4dCHCQ&usg=AFQjCNHCsjYXYh8CwkqnJTLyPGCJ7Fjs6w&sig2=eLJaAi9kvDrWWJMrDCDlbQ) I haven't finished reading, but looks like it could be summarized to at least partially answer this question.2010-08-03
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    Is it actually doable with squares, or only with non-square rectangles?2010-08-03
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    @Isaac: I actually don't know. I've only seen the rectangles example so far, so I've edited the question.2010-08-03
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    I wondered because the rectangles and ellipses are essentially the same diagram and perhaps the symmetry of squares would get in the way like the symmetry of circles does.2010-08-03
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    @Isaac: It is possible to create a Venn diagram with four squares. I sketched a quick example: http://a.imageshack.us/img230/3009/venn4squares.jpg2010-08-04
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    You will probably find interesting the following online paper: "A survey of Venn diagrams", by Frank Ruskey and Mark Weston, it is one of the dynamic surveys of the Electronic Journal of Combinatorics, available at: http://www.combinatorics.org/Surveys/ds5/VennEJC.html2011-05-10
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    My question is: is it technically still called a Venn diagram if you're using 4 elipses or squares to achieve the overlap between regions? I always thought that a Venn diagram required all regions to have 1 overlap with each of the other regions. If you have to use elipses to achieve that, I thought it became a Euler diagram. Is my assumption correct?2018-12-03

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