Very neat, from a theoretical perspective. Doing the work on the printer with postscript was a neat hack that I'm not sure I'd have thought of.

Unfortunately, the reason one would use a Venn diagram in the first place is to provide an accessible, "at-a-glance" insight regarding set overlap. The 12-set diagram linked at the bottom of the article fails at this task miserably.

In my opinion these are not higher-order Venn diagrams, but just Venn diagrams with a higher number of sets than 3.

What I image a higher-order Venn diagrams are about is Venn diagrams whose elements are lower-order Venn diagrams as elements instead of sets (just as higher-order homotopies or higher-order categories).