Geissinger defined the valuation polytope as the set of all $[0,1]$-valuations on a finite distributive lattice. Dobbertin showed the valuation polytope is equivalently defined as the convex hull of vertices characterized by all the chains of a given poset. In this project, we study the valuation polytope, $\operatorname{VAL}(P)$, arising from a poset $P$ of height two on $n$ elements. We consider height two posets, generally, and the zig-zag poset and complete bipartite poset, specifically. We will present results on normalized volumes, the existence of unimodular triangulations, and $f$-vectors. An important ingredient is an associated graphical matroid which we highlight throughout the talk. This is joint work with Federico Ardila, Jessica De Silva, Jose Luis Herrera Bravo, and Andr\'{e}s R. Vindas-Mel\'{e}ndez.
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