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Once upon a time, ages ago, long before Wikipedia. Before even the web, I used to try to invent four-set and five-set Venn diagrams. They were intended for things like mapping the quasi-elemental planes in D&D, or for coming up with new alchemical systems for D&D. I never succeeded. Today a quick google search produced this:
and this
The reason the 5-set version looks better is that 5 is prime, and there are only nice solutions with rotational symmetry for prime numbers of sets. Not that said solutions are easy to find. I was reminded to look up symmetrical Venn diagrams because they now go up to 11, but with 11 sets, there are 2^11-1 = 2047 intersections, so its kinda complex:
and this
The reason the 5-set version looks better is that 5 is prime, and there are only nice solutions with rotational symmetry for prime numbers of sets. Not that said solutions are easy to find. I was reminded to look up symmetrical Venn diagrams because they now go up to 11, but with 11 sets, there are 2^11-1 = 2047 intersections, so its kinda complex:
