In this note we give a brief review of the construction of a toric variety $\mathcal{V}$ coming from a genus $g\,\ge \,2$ Riemann surface ${{\sum }^{g}}$ equipped with a trinion, or pair of pants, decomposition. This was outlined by J. Hurtubise and L. C. Jeffrey. A. Tyurin used this construction on a certain collection of trinion decomposed surfaces to produce a variety $D{{M}_{g,}}$ the so-called Delzant model of moduli space, for each genus $g$. We conclude this note with some basic facts about the moment polytopes of the varieties $\mathcal{V}$. In particular, we show that the varieties $D{{M}_{g}}$ constructed by Tyurin, and claimed to be smooth, are in fact singular for $g\,\ge \,3$.