Find a symmetric Venn diagram for n=11, or prove that
no such diagram exists.
How many symmetric Venn diagrams are there for n=7?
How many of these are simple?
Is it true that every simple Venn diagram of
n curves can be extended to a simple Venn diagram of
n+1 curves by the addition
of a suitable curve?
[That this is true is a conjecture of Winkler
This was proven to be true for not necessarily simple Venn diagrams by
Chilakamarri, Hamburger, and Pippert
Equivalently: Is every planar dual graph of a simple Venn diagram
Find a 6-Venn diagram in which each curve is a triangle.
[There is a simple symmetric 5-Venn diagram in which
each curve is a triangle; see Grunbaum and Winkler
Find a 6-Venn diagram in which each curve is a rectangle.
These problems are both from Grünbaum
Find a 6-Venn diagram made from equilateral triangles.
Even the problem of finding a 6-Independent family made from
equilateral triangles is open.
This problem from Grünbaum
Find a Brunnian link whose minimal projection is a symmetric
Venn diagram of order 7 or prove that no such link exists.
Find a symmetric k-fold (k > 1) Venn diagram on
Note the such a diagram cannot exist on the plane since there is only
one unbounded region.