I’ve long been a fan of the order 7 Venn diagrams over at combinatorics.org, so I thought I’d try my hand at them.
Here’s a point set for the Victoria presentation.
In[]:=
pp={{-577,61},{-475,-139},{-281,-177},{-235,-187},{-233,-237},{-219,-327},{-159,-329},{-121,-329},{-89,-379},{-15,-445},{77,-317},{137,-195},{251,-211},{453,-147},{331,9},{255,61},{281,127},{305,175},{265,197},{231,213},{211,257},{205,345},{125,305},{-19,185},{-221,225},{-503,191},{-577,61}};​​colors={Red,Orange,Yellow,Blue,Green,Purple,Cyan};
Here’s code for the Victoria presentation of Venn-7.
In[]:=
Graphics[Table[{Opacity[.3],colors[[k+1]],EdgeForm[Black],FilledCurve[ResourceFunction["CubicSplineCurve"][RotationMatrix[2Pik/7.].#&/@pp,SplineClosed->True]]},{k,0,6}]]
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That page also shows a solution in quadrilaterals. Perhaps not as obvious, but I’ve tried to make the colors match up.
In[]:=
quad={{-605,-358},{270,-373},{404,191},{-77,442}};​​Graphics[Table[{Opacity[.3],colors[[k+1]],EdgeForm[Black],Polygon[RotationMatrix[2Pi(k-1)/7.].#&/@quad]},{k,0,6}]]
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And now a Venn ghost for Halloween.
In[]:=
Graphics[{FilledCurve[ResourceFunction["CubicSplineCurve"][RotationMatrix[2Pi5.5/7.].#&/@pp,SplineClosed->True]],White,Disk[{23,402},40],Disk[{-160,402},40]}]
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And here’s a Venn-5 with filling.
In[]:=
pp=RootReduce[2CirclePoints[5]/(EuclideanDistance@@CirclePoints[5][[{1,2}]])];​​sp=Join[Table[2.12CirclePoints[10][[Mod[n-2,10,1]]]+pp[[2]],{n,1,9}],Table[1.05CirclePoints[10][[Mod[n-6,10,1]]]+pp[[4]],{n,1,7}]];​​Graphics[{AbsoluteThickness[2],EdgeForm[Black],Table[{Opacity[.3],colors[[k+1]],FilledCurve[BSplineCurve[sp.RotationMatrix[2kPi/5],SplineClosed->True]]},{k,0,4}]},ImageSize->600]
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CITE THIS NOTEBOOK

Order 7 Venn diagrams​
by Ed Pegg​
Wolfram Community, STAFF PICKS, October 6, 2025
​https://community.wolfram.com/groups/-/m/t/3557090