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7:42 AM
Just did some googling on venn diagramms (of k sets): I didnt expect there to be so much structure: Apparently a "nice" rotationally symmetric Venn diagram exists if and only if k is prime. ("nice" means that all sets have a Jordan curve boundary and all segments are simply connected - I hope I got these conditions right:)
*path connected, not simply-
 
 
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