I've been interested in high dimensional venn diagrams lately. I present the work I've found for n=4,5,6,7 and 11.

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n=3s and 4s n=4 n=5 n=5 n=5 n=5 n=5 n=5 n=5 n=5 n=6 n=7 n=7 n=7 n=7 n=7 n=11