  We give a myriad of examples of extremal divisors, rigid curves, and
birational morphisms with unexpected properties for the Grothendieck--Knudsen
moduli space $\bar M_{0,n}$ of stable rational curves. The basic tool is an
isomorphism between $M_{0,n}$ and the Brill--Noether locus of a very special
reducible curve corresponding to a hypergraph.
