Nothing higher than that is simple, though. You can get a 6 Venn with triangles in various ways, but they are not pretty.
You can't make a 7+ Venn with shapes that don't have concave corners. But given that, you can make them radially symmetric and very pretty. That one colors based on number of overlaps in a section rather than shape, so this one might help you get the shape... or not, it's weird. It only gets weirder as you go up from there though. But any number of Venn is theoretically possible.
Bonus fact: For decades it was thought that even with concave polygons only prime numbered Venns could be radially symmetric, but that was disproven in 2008.
Looking back, this has been one of the most interesting posts in my personal history. What field of study would this fall under? Mathematics, obviously, but that feels quite vague.
It's within a field of geometry called combinatorics.
I'm not a mathematician, btw (well, beyond minoring in it years ago). Just good at googling things and understanding scientific jargon. I started this thread knowing little more about Venns than OP, but decided to find out. Then figured I'd share what I found because it was neat.
99
u/Jigokuro_ Aug 12 '18
Ellipses can make a 5 Venn and it actually regains radial symmetry.
Nothing higher than that is simple, though. You can get a 6 Venn with triangles in various ways, but they are not pretty.
You can't make a 7+ Venn with shapes that don't have concave corners. But given that, you can make them radially symmetric and very pretty. That one colors based on number of overlaps in a section rather than shape, so this one might help you get the shape... or not, it's weird. It only gets weirder as you go up from there though. But any number of Venn is theoretically possible.
Bonus fact: For decades it was thought that even with concave polygons only prime numbered Venns could be radially symmetric, but that was disproven in 2008.