To each graded poset one can associate two sequences of numbers: the Whitney numbers of the first kind and the Whitney numbers of the second kind. One sequence keeps track of the M$\ddot{\text{o}}$bius function at each rank level and the other keeps track of the number of elements at each rank level. We say if $P$ and $Q$ are Whitney duals if the Whitney numbers of the first kind of $P$ are the Whitney numbers of the second kind of $Q$ and vice-versa. In this talk, we will discuss a method to construct Whitney duals. This method uses a new type of edge labeling as well as quotient posets. For posets which have this type of labeling, one can construct a simplicity complex whose $f$-vector encodes the Whitney numbers of the second kind of this poset. Time permitting, we will discuss this complex. This is joint work with Rafael S. Gonz\'alez D'Le\'on.