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Oct 22, 2010 at 11:27 vote accept Brendan Foreman
Oct 21, 2010 at 12:35 comment added Gerry Myerson @Qiaochu, you are right, to get $n$-choose-4 you must arrange that no three lines meet at a non-vertex point. Of course, that's easily done; if three meet, just move one vertex a tiny bit.
Oct 21, 2010 at 11:30 comment added Qiaochu Yuan This isn't enough; for example, if the vertices lie at the nth roots of unity then lots of edges will intersect at the origin. You need some kind of general position requirement.
Oct 21, 2010 at 10:48 history answered Gerry Myerson CC BY-SA 2.5