TITLE: Lower bound of crossing number (minimum) of K7
QUESTION [5 upvotes]: I am able to construct K7 with crossing number 9 from K6 with crossing number 3. Hence, I know the crossing number for K7 is at most 9; though, the number may not be sharp.
Now, I heard it is possible to prove the crossing number of K7 is at least 7 (also, may not be sharp). Anyone have any idea?

REPLY [4 votes]: Take a look at the Rectilinear Crossing Project for the current state of the art. Tight bounds and solutions are known up to $K_{27}$.
There are 3 essentially different ways to embed $K_7$ with 9 crossings, and these solutions are available at that site.
I've added this info at the Wikipedia crossing number page -- really should have been there.