# Is it possible to create rotationally symmetric Venn diagrams with 7 sets?

I need to construct a two-dimensional Venn diagram with 7 sets. The examples I found on-line do not have rotational symmetry, so they are rather confusing to use. Is there a way to construct these in a way which is rotationally symmetrical?

If you are looking for a rotationally symmetric Venn diagram which divides the region into $2^n$ regions, the article here addresses it for the case $n=7$.

Here is one such rotationally symmetric Venn diagram taken from here.

Typically, though when I think of a rotationally symmetric Venn diagram with $n$ sets, I would construct $n$ circles, where the $k^{th}$ circle is given by $$(x- r\cos(k \theta))^2 + (y-r\sin(k \theta))^2 \leq cr^2$$ where $\theta = \dfrac{2 \pi}n$ and $k \in \{0,1,2,\ldots,n-1\}$. Below is one such construction with $c = 1.5$ for $n=7$. However, as Martin rightly points out in the comments, this doesn't divide the region into $2^n$ distinct sub-regions.

PS: The figure was done with grapher on Mac OS X

• Isn't a Venn diagram supposed to have $2^n$ regions? Jan 12, 2013 at 8:05
• @Martin Thanks for pointing that out. I did not know that in a Venn diagram, we needed to have all the $2^n$ regions i.e. I did not know the difference between the Venn diagram and the Euler diagram. This is a good piece of information to know. Thanks.
– user17762
Jan 12, 2013 at 8:18