  For any northeast path $\nu$, we define two bivariate polynomials associated
with the $\nu$-associahedron: the $F$- and the $H$-triangle. We prove
combinatorially that we can obtain one from the other by an invertible
transformation of variables. These polynomials generalize the classical $F$-
and $H$-triangles of F. Chapoton in type $A$. Our proof is completely new and
has the advantage of providing a combinatorial explanation of the relation
between the $F$- and $H$-triangle. We also show that the specialization of this
$F=H$ correspondence at $x=y$ is a special case of a general $f=h$ reciprocity
result for abstract simplicial complexes, uncovering a clear explanation of the
nature of this result. Interestingly, this connection leads to an elementary
proof of Klee's Dehn-Sommerville relations, as well to a generalization in the
context of simplicial homology manifolds and reciprocal complexes.
