Let *P=P*_{0},P_{1},P_{2},P_{3} be a partition of *{1,...,n}* into four nonempty subsets. Fix four (arithmetic) genus zero at worst nodal curves *C*_{j} for *j=0,1,2,3*, and *#(P*_{j}) marked points on each curve. We call the curves *C*_{j} the tails. Mark one additional point *x*_{j} on each tail. Next, consider *ℙ*^{1} with four marked points, *y*_{0},...,y_{3}; we call this the spine. Glue the four tails to the spine by identifying *x*_{j} and *y*_{j}. Then, as the cross ratio of *y*_{0},...,y_{3} varies, we sweep out a curve *F*_{P} in *M*_{0,n}.

The homology class of *F*_{P} only depends on the partition *P*, and not on the choice of the tails *C*_{j} or the choices of marked points. The classes of the F-curves span *H*_{2}(M_{0,n},Q).

If we only consider F-curves up to *S*_{n} symmetry, then it is enough to keep track of the four integers *#(P*_{0}), *#(P*_{1}), *#(P*_{2}), *#(P*_{3}).