Monotone Symmetric Venn diagrams
without polar symmetry
There are (at least) 17 of them, which we call M1M17.
These are believed to be all of them.
Those numbered M12M17 show Tutte embeddings of the diagrams.

M1.
This one has the zigzag middletwolevels and the rather nice property
that each curve interects the others exactly 6 times. It was
discovered by Carla Savage and Peter Winkler.

M2.
This one was discovered by Branko Grünbaum (Figure 6 of
[Br92b]).
 M3
 M4
 M5
 M7
 M8
 M9
 M10
 M11
 M12
 M13
 M14
 M15
 M16
 M17
The numbers above are simply the order in which our program
found them.
We have seen none of these published before, except for M1 and M2.